curve #3

y² + y = x³ − 2248232106757x + 1329472091379662406

a-invariants: [0, 0, 1, -2248232106757, 1329472091379662406]
c-invariants: [107915141124336, -1148663886952028319000]
rank (lower bound): ≥ 14
torsion subgroup: trivial
conductor (N): 36275332432131715984679943280544970923
discriminant (Δ): -36275332432131715984679943280544970923
Faltings height: 5.9864
naive height: 96.9858
primes of bad reduction: 1217, 381991, 78031093338905335441668500509
regulator: 9265899869259.67785615968081224333780816023564040627142679366174481
submitted by: David Renshaw
submitted at: 2026-05-27 22:11:44 UTC
last updated: 2026-07-01 22:43:37 UTC

(-1715883, 367667174)
(-1695357, 517854321)
(-1684243, 581714825)
(-1664989, 676084814)
(-1647951, 747688353)
(-1621373, 844007025)
(-1611950, 874669467)
(-1579846, 968593731)
(-1557343, 1026493950)
(-1524175, 1102427297)
(-1494242, 1163010071)
(-1459188, 1226017574)
(-1373814, 1351013139)
(-1366017, 1360736678)

Found by Mestre (1986). A historical rank ≥ 14 record, via Dujella's elliptic-curve rank-records tables.

last edited by David Renshaw at 2026-05-27 22:31:35 UTC · history