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curve #5767

y² = x³ − 2466123524659025x

a-invariants: [0, 0, 0, -2466123524659025, 0]
c-invariants: [118373929183633200, 0]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 7784659505762115439670417856800
discriminant (Δ): 959896596931022583227984920559647024563881000000
Faltings height: 7.8964
naive height: 117.9379
primes of bad reduction: 2, 5, 7, 11, 17, 73, 373, 1597, 1733
regulator: 394116957.8584534461729420934232530345465158453840732125785
submitted by: Michael Rubinstein
submitted at: 2026-10-24 21:26:53 UTC
last updated: 2026-10-24 21:26:53 UTC

Witness: 10 independent points log in to add more points →

(-34789975, 209018169800)
(-7465975, 134148638800)
(69190025, 400748624800)
(75272855, 490779014600)
(145811295, 1655444235900)
(35356102775, 6648078716988800)
(-35088589305/3481, 31707218915641500/205379)
(739240121/4, 19359959528869/8)
(1036880320/9, 30127205747800/27)
(26676906039/361, 3226636995631812/6859)

Commentary

Rank 10, proved: 10 independent points listed, matching the 2-descent upper bound. Torsion Z/2. Member of the family y^2 = x^3 + a x.

last edited by Michael Rubinstein at 2026-10-24 21:26:53 UTC · history

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