curve #338

y² + xy + y = x³ + x² − 855631467438096021846442064975x + 305451237205254133961575716954767187528207317

a-invariants: [1, 1, 1, -855631467438096021846442064975, 305451237205254133961575716954767187528207317]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 7574847575418925340475858758748628717526303842283563568546909495282010
naive height: 218.3839
Faltings height: 16.0093
discriminant (Δ): -215413766000126800466521720643100270220386334713211058780295465294633003146387305267200000
primes of bad reduction: 2, 3, 5, 7, 13, 19, 23, 571, 168062882960819311, 26568118382242454987, 191565698149509818162191
regulator: 4806019132545962067.726863555523846378628942727716867807241275704607592758426
submitted by: 7fff-zip
submitted at: 2026-08-24 19:18:51 UTC
last updated: 2026-08-24 19:18:51 UTC

Witness: 19 independent points

(9586890724415387, -934461935779114035454094)
(8129199673154331, -728394792241420409231246)
(28638444903465715/9, -4661113179977735938988794/27)
(134171279221871019/49, -46643764194443056548488258/343)
(3256072716032883114945/18861649, 1045478165108203724934815689773236/81916141607)
(196422946210587, 12040098259551536392306)
(618098292242515495/1156, 35547451921105752406539239/39304)
(1515067690314950403/2809, 138277234466923643715010442/148877)
(10261352988409163507/17161, 6205345600399569582765904646/2248091)
(8526007895786033103/13924, 5477212901272398822592722877/1643032)
(525938758437357743295963/314104729, 332487529501471124969436533792234822/5566878112067)
(60870243559983964753275/5230369, 14971790245713584704853356591836718/11961853903)
(10948352583275087, 1141611825337244763630806)
(53474554257282331, 12363920614128437121059954)
(973293186721147, 19866333665769180644786)
(4170049028301701579771133/12362548969, 10213884019127964331583983597024492078/1374554732216203)
(158181893980577376691427/3682561, 62897773204253778267905078224857694/7066834559)
(146263678576776715/9, -55849027876027769835255794/27)
(-82454096071542520301/677329, 11257106036780956728997042947158/557441767)

Commentary

New in this search: Mestre quartic family with roots [0,158,863,928,3783,3850], T=9037/2. 19 independent rational points certified exactly by Cremona-Brumer quadratic characters; quartic point box [10000000,10000].

last edited by 7fff-zip at 2026-08-24 19:18:51 UTC · history