curve #6156

y² + xy + y = x³ − x² − 146092556837146590906974030x + 612981848421804706924745575738884085597

a-invariants: [1, -1, 1, -146092556837146590906974030, 612981848421804706924745575738884085597]
c-invariants: [7012442728183036363534753425, -529616317036407710790703353774759943565625]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 559447334357790496599073662977426523846207507784294995150
discriminant (Δ): 37233154484535096496795062233824479562515805898776454513939638621448995584000000
Faltings height: 14.0022
naive height: 192.3525
primes of bad reduction: 2, 3, 5, 7, 11, 23, 71, 191, 154291, 28624205431, 11720938414325923058883403637417
regulator: 13292365026943874.68124955077984636962709612256909898995608339499135824937328
submitted by: apkorte
submitted at: 2026-10-29 19:08:53 UTC
last updated: 2026-10-29 19:08:53 UTC

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

(4410027516109, -7380881508280469605)
(11520618762329, 21423704630464017235)
(-4307364367091, -34093098623161983205)
(8746824440569, -2080546385535903085)
(-5382563856791, 35261749083075666995)
(4990796733529, 2859126340963921235)
(32596123945369, 174598237645303525715)
(-1600279419671, -29028823050949185565)
(1869200930119, 18612799206095455715)
(4800585019753, -4720653845365336525)
(-12373530045431, -22939534012505241085)
(-2609975904167, 31249014296921407571)
(9520697956369, 9223331469533080715)
(-11359274095031, 28403611156032966515)
(37557430209851/4, -66468767916478581055/8)
(-105548614081439/9, 721115684986206660545/27)
(8949929875409, 4729079271064589795)
(4359061341619, 7680086920038644465)
(9853056567569, -11405494411332090485)

Commentary

Specialization at T = 11/5 of the rank-16 fibration of X1008 given in curve#3762. 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 2026-10-29 19:08:53 UTC · history