curve #6030

y² + xy + y = x³ − x² − 883079936634503444924967x + 331137954698729780750216713137038175

a-invariants: [1, -1, 1, -883079936634503444924967, 331137954698729780750216713137038175]
c-invariants: [42387836958456165356398401, -286103192859511785301874187406297190625]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 4007383167207271599881499506623453435050385271176739577779054
discriminant (Δ): -3296060669554050015368683381814754064586482571968180774314059193671902208
Faltings height: 12.6806
naive height: 177.0988
primes of bad reduction: 2, 7, 13, 37, 107, 6977, 797141201500893134662305029470820990225846787620179
regulator: 897873341989003830.0826642229561791747227408643806012389780931941749079998731
submitted by: apkorte
submitted at: 2026-10-28 14:06:36 UTC
last updated: 2026-10-28 14:06:36 UTC

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

(-468738313073, 801300572523444690)
(511683238491, 115106319014370926)
(735441462271, -281896849571529314)
(581775772905, 119553230616947754)
(146684816801, -452503852740358604)
(2050151370055, -2671652939457954210)
(193476664923, 409298142002036334)
(2222423561419, -3057038937267934650)
(659363595315, -188500570397967586)
(47968853721, 537482998306454442)
(301338115503, 303965662925626034)
(534195599907, 108817162307479950)
(99796169395751/121, -538745989353330726278/1331)
(-204818428845, 709518774593886590)
(25735869221551/4, -129241387468225118985/8)
(477880013035, -135147678453186066)
(1227695578163, 1047573786816176302)
(-16564727210221/25, -98849937575192742418/125)
(107331383840327/121, 659836773125889422662/1331)

Commentary

Specialization at T = 1/7 of the rank-17 fibration of X1008 given in curve#3594. 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 2026-10-28 14:06:36 UTC · history