curve #5667

y² = x³ + x² − 92164715012578470955501685508x + 10370039947036129174642184091603982621953888

a-invariants: [0, 1, 0, -92164715012578470955501685508, 10370039947036129174642184091603982621953888]
c-invariants: [4423906320603766605864080904400, -8959714514239242150328770677745476169853585600]
rank (lower bound): ≥ 22
torsion subgroup: trivial
conductor (N): 361495350880784086493067674065355732156988037039067129366685430059641748487800
discriminant (Δ): 3647889205628448750737425539210582256184410687650085884196601263454979420726024062880000
Faltings height: 15.5662
naive height: 211.6937
primes of bad reduction: 2, 3, 5, 11, 13, 278549, 13301221, 131852849, 1495414619, 15758154692718817, 365987131830639437154674177
regulator: 11342716177633955073935.27501698958257105006404229839541180246227371043094311524293
submitted by: apkorte
submitted at: 2026-10-24 03:10:41 UTC
last updated: 2026-10-24 03:10:41 UTC

Witness: 22 independent points log in to add more points →

(146834041031118, 53841627023916349530)
(-281495442190302, 3742776679764441818070)
(257373683775198, 1923021779243933369430)
(144618086920418, -256815897498807160470)
(3334058444485596/25, 83913618426345050278056/125)
(-1718481610692, 3244752415817889495480)
(40643698759038, 2586747915120861951030)
(231660846597243, -1204810475132422080780)
(-346027066341582, -911080852699292877030)
(3502024853507478, -206487441125099605343070)
(129648587347368, -774755664019531056720)
(4452216786615258, 296399927655493315955730)
(92320147212954, 1627336900733585606994)
(2575329782423058, 129820783044945073923270)
(138126037621419, -524378121034817690784)
(205878782857518, 348817666872515689530)
(214084691004888, -671542660736699246280)
(465605829954783, -8270171418785306903730)
(23590450002082008, 3623001755268754211840520)
(105359212266127308/841, -21677305223741586529762080/24389)
(1049311733075838, -32695727123308064703030)
(202991048609724, 160462509913392522264)

Commentary

Specialization at T = 89/57 of the rank-17 fibration of X1152 given in curve#846. 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 2026-10-24 03:10:41 UTC · history