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curve #5737

y² = x³ + 1584575252935983x

a-invariants: [0, 0, 0, 1584575252935983, 0]
c-invariants: [-76059612140927184, 0]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 8927568825660922670440875293472
discriminant (Δ): -254635283340450958665869105455822142425568453568
Faltings height: 7.7858
naive height: 116.6109
primes of bad reduction: 2, 3, 7, 11, 37, 43, 53, 113, 317, 757
regulator: 2974216967.438898461697158073412338948877172964727597181687
submitted by: Michael Rubinstein
submitted at: 2026-10-24 18:03:09 UTC
last updated: 2026-10-24 18:03:09 UTC

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

(16224201, 173144673072)
(40803057, 364126480668)
(108127327, 1198127108332)
(132840631, 1598338472192)
(940951/9, 347523314732/27)
(1994337/4, 224879445783/8)
(36729583/9, 2182616398864/27)
(20638986361/100, 3019699160200891/1000)
(454423645809/256, 306408321472446711/4096)
(596103993639/11449, 579338976057265116/1225043)

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 18:03:09 UTC · history

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