curve #4349

y² = x³ − x² − 2258742409x + 26621829718729

a-invariants

[0, -1, 0, -2258742409, 26621829718729]

c-invariants

[108419635648, -23000610359168000]

rank (lower bound)

≥ 6

torsion subgroup

ℤ/2ℤ × ℤ/2ℤ

conductor (N)

656795382758592

discriminant (Δ)

431380174813005369419749822464

Faltings height

4.3887

naive height

76.2278

primes of bad reduction

2, 3, 7, 11, 23, 29, 43, 61, 67, 379

regulator

1771.6931811210896756374316286309963254912369867042

submitted by

Volkan Dagli

submitted at

2026-10-17 10:05:49 UTC

later contributions

(45199, 4106844)
(347641, 203113680)
(40705, 1456728)
(-1983, 5576120)
(-18179/4, 48526023/8)
(-7175, 6516048)

BASE torsion/torsion_Z2xZ2.tsv.gz:138 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 10:05:49 UTC · history