EXHIBIT 5.1 and 23.4

Davis Polk & Wardwell LLP

900 Middlefield Road

Redwood City, CA 94063

davispolk.com

OPINION OF DAVIS POLK & WARDWELL LLP

September 17, 2025

CoreWeave, Inc.

290 W Mt. Pleasant Ave., Suite 4100

Livingston, New Jersey 07039

Ladies and Gentlemen:

We have acted as counsel to CoreWeave, Inc., a Delaware corporation (the “Company”), in connection with the merger contemplated by Agreement and Plan of Merger, dated as of July 7, 2025 (the “Merger Agreement”), by and among the Company, Miami Merger Sub I, Inc. (“Merger Sub”), a Delaware corporation and a wholly owned subsidiary of the Company, and Core Scientific, Inc., a Delaware corporation (“Core Scientific”), pursuant to which Merger Sub will merge with and into Core Scientific, with Core Scientific surviving as a wholly owned subsidiary of the Company (the “Merger”) and the preparation and filing of the Company’s Registration Statement on Form S-4 (File No.333-289742), including the proxy statement/prospectus forming a part thereof (the “Registration Statement”) filed with the Securities and Exchange Commission under the Securities Act of 1933, as amended (the “Securities Act”), relating to the registration by the Company of (a) shares of the Class A common stock, par value $0.000005 per share of the Company (the “Company Common Stock”) and (b) warrants exercisable for a number of shares of Company Common Stock (the “New Tranche 1 Warrants” and “New Tranche 2 Warrants” (each as defined in the Registration Statement)), in each case, to be issued in connection with the Merger. We refer to the maximum number of shares of Company Common Stock that are issuable upon exercise by holders of the New Tranche 1 Warrants and New Tranche 2 Warrants as the “Underlying Securities.”

We, as your counsel, have examined originals or copies of such documents, corporate records, certificates of public officials and other instruments as we have deemed necessary or advisable for the purpose of rendering the opinions expressed herein.

In rendering the opinions expressed herein, we have, without independent inquiry or investigation, assumed that (i) all documents submitted to us as originals are authentic and complete, (ii) all documents submitted to us as copies conform to authentic, complete originals, (iii) all signatures on all documents that we reviewed are genuine, (iv) all natural persons executing documents had and have the legal capacity to do so, (v) all statements in certificates of public officials and officers of the Company that we reviewed were and are accurate, (vi) all representations made by the Company as to matters of fact in the documents that we reviewed were and are accurate, (vii) the Registration Statement, as then amended, will have become effective under the Securities Act and such effectiveness will not have been terminated or rescinded or be subject to any stop order, (viii) the stockholders of Core Scientific will approve, among other things, the adoption of the Merger Agreement and any ancillary documents thereto, and all transactions (including the Merger) contemplated therein in accordance with the General Corporation Law of the State of Delaware (“DGCL”) and (ix) all other necessary action will have been taken under the DGCL to authorize and permit the Merger, and the Merger shall have been consummated, or will be consummated concurrently with, the issuance of the Company Common Stock, New Tranche 1 Warrants and New Tranche 2 Warrants. As to any facts material to the opinions expressed herein that we did not independently establish or verify, we have relied upon statements and representations of officers and other representatives of the Company and others and of public officials.

Based upon the foregoing, and subject to the assumptions, qualifications and limitations set forth herein, we advise you that, in our opinion:

The Company Common Stock, when issued and delivered as contemplated in the Registration Statement and in accordance with the terms and conditions of the Merger Agreement, will be validly issued, fully paid and non-assessable.

Assuming that the warrant agreement governing the New Tranche 1 Warrants and New Tranche 2 Warrants (the “Warrant Agreement”) and the New Tranche 1 Warrants and New Tranche 2 Warrants have been duly authorized by the warrant agent, when the Warrant Agreement has been duly executed and delivered by the warrant agent and the Company, and such New Tranche 1 Warrants and New Tranche 2 Warrants have been duly executed and delivered in accordance with the Warrant Agreement and applicable agreement against payment thereto, the New Tranche 1 Warrants and New Tranche 2 Warrants when issued as contemplated in the Registration Statement and in accordance with the terms and conditions of the Merger Agreement and the Warrant Agreement, will constitute valid and binding obligations of the Company, enforceable in accordance with their terms, subject to applicable bankruptcy, insolvency and similar laws affecting creditors’ rights generally, concepts of reasonableness and equitable principles of general applicability; provided that we express no opinion as to the validity, legally binding effect or enforceability of any provision in the New Tranche 1 Warrants and New Tranche 2 Warrants that require or relate to adjustments to the exercise price at a price or in an amount that a court would determine in the circumstances under applicable law to be commercially unreasonable or a penalty or forfeiture.

The Underlying Securities, when issued upon exercise by holders of the New Tranche 1 and New Tranche 2 Warrants and delivered against payment therefor in accordance with the terms and conditions of the Warrant Agreement, will be validly issued, fully paid and non-assessable.

We are members of the Bar of the States of New York and California and the foregoing opinion is limited to the laws of the State of New York and the DGCL.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement and further consent to the reference to our name under the caption “Legal Matters” in the proxy statement/prospectus which forms a part of the Registration Statement. In giving this consent, we do not admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act.

Very truly yours,

/s/ Davis Polk & Wardwell LLP