curve #6353

y² = x³ + 69089596801

a-invariants: [0, 0, 0, 0, 69089596801]
c-invariants: [0, -59693411636064]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/3ℤ
family: y² = x³ + k (Mordell curves)
conductor (N): 7461676454508
discriminant (Δ): -2062096870805891755315632
Faltings height: 3.3444
naive height: 63.4405
primes of bad reduction: 2, 3, 31, 61, 139
regulator: 248252.779822652135761398243398428956641132541228
submitted by: apkorte
submitted at: 2026-11-01 05:41:26 UTC
last updated: 2026-11-01 05:41:26 UTC

Witness: 5 independent points log in to add more points →

(-3525, 159026)
(87615, 25935224)
(10980447103/106929, 1150651718239996/34965783)
(-69249/49, 88296340/343)
(192472251/4225, 2671227135374/274625)

Commentary

3-isogenous to curve#6339 (the images of its points under the isogeny, moved to the minimal model). Found by Claude (Anthropic) in a scan of the isogeny classes of all leaderboard curves.

last edited by apkorte at 2026-11-01 05:41:27 UTC · history