curve #4309

y² + xy = x³ + x² + 8425949699x − 74923005839201

a-invariants

[1, 1, 0, 8425949699, -74923005839201]

c-invariants

[-404445585527, 64736510386961179]

rank (lower bound)

≥ 9

torsion subgroup

ℤ/2ℤ

conductor (N)

293853198970733402778

discriminant (Δ)

-40710937827538684703980712126058

Faltings height

4.7545

naive height

80.1773

primes of bad reduction

2, 3, 61, 73, 79, 97, 109, 673, 1993, 9817

regulator

316229537325.91491170193279157635812893796091640924622113

submitted by

Volkan Dagli

submitted at

2026-10-17 09:47:29 UTC

later contributions

(16603913/64, 71564294953/512)
(5079759/4, 11473509767/8)
(27516891/625, 304799920361/15625)
(72672939/625, 776728252313/15625)
(2351543580697/18740241, 4407289711064825876/81126503289)
(3616981/225, 27116490076/3375)
(1067551838760203/82841503684, 142509573081657413000647/23843607273336248)
(139638137346805681/11427915470400, 210862332341312320855850269/38632296805996608000)
(139709730353231/3825298801, 3965427802258550619701/236590905543049)

Rational 2-isogeny of 2-9.ec from Layr Labs / Yukon Elliptic Rank Challenge via pCwOrM Werr Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 09:47:29 UTC · history