curve #51

y² = x³ + 90389647280869401176648335x

a-invariants: [0, 0, 0, 90389647280869401176648335, 0]
c-invariants: [-4338703069481731256479120080, 0]
rank (lower bound): ≥ 13
torsion subgroup: ℤ/2ℤ
conductor (N): 261449226737919396153756025756944483500777736264711200
discriminant (Δ): -47264606773393166969536680533142442422985196847451054883198340996443105471704000
Faltings height: 13.9776
naive height: 190.9121
primes of bad reduction: 2, 5, 7, 23, 43, 83, 97, 101, 269, 461, 503, 4013, 12829
regulator: 138756719389405.4255918300409526821899187152598720710262995061562
submitted by: David Renshaw
submitted at: 2026-05-28 20:49:27 UTC
last updated: 2026-07-01 22:45:39 UTC

(109267165625, 3142916660550827000)
(699012151740, 7970257947656823630)
(1422638553735, 11466083720951564040)
(3291776981199, 18254084011425711708)
(5654458993409, 26303878853294220788)
(7605531940860, 33576727388672968290)
(7907148183375, 34772156979673232700)
(9195899733104, 40110615271804927948)
(13086347270535, 58514440970809001640)
(22835291094000, 118201304172014979300)
(27155267727809, 149930257416935566012)
(35526638964665, 219205169249540459320)
(48336648553881, 342497307164478802176)

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