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curve #1656

y² + y = x³ + x² − 163451383190620x + 804372734093089612756

a-invariants: [0, 1, 1, -163451383190620, 804372734093089612756]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/5ℤ
conductor (N): 111635625800985
discriminant (Δ): -33923913569676056976412138510141486096875
Faltings height: 6.8299
naive height: 109.7963
primes of bad reduction: 3, 5, 11, 13, 17, 29, 1789, 59009
regulator: 613.748226770722301498660708115069562689950956957
submitted by: Michael Rubinstein
submitted at: 2026-09-25 02:30:28 UTC
last updated: 2026-09-25 02:30:28 UTC

Witness: 5 independent points log in to add more points →

(8204080, 3949177732)
(224956460, 3368686483012)
(9858095, 12291595552)
(28580957/4, 9014701703/8)
(7436885, 342594037)

Commentary

Torsion Z/5. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 02:30:28 UTC · history

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