curve #6234

y² = x³ − 20375192786989004076x + 35344454359350500469174740560

a-invariants: [0, 0, 0, -20375192786989004076, 35344454359350500469174740560]
c-invariants: [978009253775472195648, -30537608566478832405366975843840]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 1056738254468057369589312
discriminant (Δ): 1691185507118640834738870867142462921826635458033486987264
Faltings height: 9.8730
naive height: 144.9962
primes of bad reduction: 2, 3, 23, 47, 59, 131, 347, 491, 11329, 113761
regulator: 12885076447.454587845006430024623161706607816319141883033
submitted by: apkorte
submitted at: 2026-10-31 11:26:46 UTC
last updated: 2026-10-31 11:26:46 UTC

Witness: 9 independent points log in to add more points →

(181054008569/64, -9497422933791885/512)
(689859467249/196, -233365826366797545/2744)
(338797805902209/4, -6236068586457745863905/8)
(412232729874/121, 98455581685716800/1331)
(79172401361/16, 15102239969578905/64)
(24677663510969/8464, 20941735002494722515/778688)
(4744490227569/1600, 2023684244733071497/64000)
(4901363124259865/56644, 342685295561452042278045/13481272)
(3516136930226/1225, -967232194656076224/42875)

Commentary

2-isogenous to curve#6082 (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 2026-10-31 11:26:46 UTC · history