curve #5549

y² = x³ + x² − 319814184033439765051835665x + 2197617713078239238715758018587354824275

a-invariants: [0, 1, 0, -319814184033439765051835665, 2197617713078239238715758018587354824275]
c-invariants: [15351080833605108722488111936, -1898741704099690808735416558711809496845184]
rank (lower bound): ≥ 20
torsion subgroup: trivial
conductor (N): 32463936289123760124668357570807899958076532012098887523634210440
discriminant (Δ): 7146629663132549749341708156813133695848453571494766879301047470837602836000000
Faltings height: 14.0186
naive height: 194.7030
primes of bad reduction: 2, 3, 5, 17, 43, 563, 1721, 104473467113063, 5001380592943952780804942426375696483
regulator: 3423748819224833066.43027756257862554532931662380018835084435122780662180012801
submitted by: apkorte
submitted at: 2026-10-23 01:18:21 UTC
last updated: 2026-10-23 01:18:21 UTC

Witness: 20 independent points log in to add more points →

(9094287496895, 6425598138152488650)
(10671932617955, 101255405153142510)
(7711369196795, 13782985598290511250)
(9676408601195, -2999171613405632850)
(6087885737795, -21823310292246191250)
(11241175322870, 4796929498294449675)
(7847960661035, -13080072376727874990)
(-1713670477705, -52351135230414957750)
(11069262812195, -3716383211459845650)
(10858244371595, 2280379665579210450)
(31963884512795, -156946782256943231250)
(8003893314059, 12272203709995499730)
(367215534323915/49, -5107868686258190448030/343)
(45470672913545, -285779286742420329750)
(14438425047695, 24289007436437603850)
(-19510981694305, -31782022894573355850)
(3099216906522005/4, 172489741691366688084225/8)
(9885153034295, 1464804291572493750)
(149590563362345/16, -318649422373902532125/64)
(11056268827295, 3632680285761170250)

Commentary

Specialization at T = -17/7 of the rank-17 fibration of X1008 given in curve#3589. 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 01:18:21 UTC · history