curve #5544

y² + xy + y = x³ − 23625352281937590183013873x + 44579850997951718276645929240564764728

a-invariants: [1, 0, 1, -23625352281937590183013873, 44579850997951718276645929240564764728]
c-invariants: [1134016909533004328784665881, -38516991262231985616386382370341133724029]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 260332908683445191166767635201796588861670376389160609605210
discriminant (Δ): -14594488527683011137078570345806038722339712573304213762567128820684609062500
Faltings height: 13.4335
naive height: 186.9038
primes of bad reduction: 2, 3, 5, 11, 13, 31, 47, 127, 1907599, 729603550901, 6801010894591, 34646630961386589799
regulator: 68572651092951259.53769083689047358553737228222808151854858743272132462452220
submitted by: apkorte
submitted at: 2026-10-23 00:19:57 UTC
last updated: 2026-10-23 00:19:57 UTC

Witness: 19 independent points log in to add more points →

(2966985684259, 775985622371160620)
(148263537260401/64, 773369283130967995915/512)
(3233662795489, -1412965197950700100)
(2031842956309, 2228244253435467770)
(89013967121634, 838595535209688886495)
(4417881192097, 5141263917024708962)
(2216136199609, -1762633481832550780)
(-1212597582356, 8452509179831465900)
(-3590814141866, -9116704611731794630)
(2156210424109, -1913993555278645030)
(2414025554209, -1270995917615862430)
(28937258496259, -153596799393339462880)
(2762004347059, 630029974642122920)
(3134987395809, 1151424990542588770)
(13130293003459, 44700048158220172220)
(-22339545291989/4, -12203107771101776465/8)
(8698365224584, -22298205388372851280)
(3696020881811866/1369, 34901210969341485990755/50653)
(3448982024809, -2030696685093105580)

Commentary

Specialization at T = -7/24 of the rank-17 fibration of X1008 given in curve#751. Found by Claude (Anthropic): a Mestre-Nagao sieve over the fibration, then a 2-covering point search seeded with its generic sections.

last edited by apkorte at 2026-10-23 00:19:57 UTC · history