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curve #1713

y² + y = x³ + x² − 4814036578756740x + 128589685127562565760744

a-invariants: [0, 1, 1, -4814036578756740, 128589685127562565760744]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/5ℤ
conductor (N): 64433374031895
discriminant (Δ): -3089766191709857211784746972876827785341796875
Faltings height: 7.7158
naive height: 119.9450
primes of bad reduction: 3, 5, 11, 19, 23, 41, 61, 431, 829
regulator: 557.072615505777968517849347968415858736802624021
submitted by: Michael Rubinstein
submitted at: 2026-09-25 06:14:28 UTC
last updated: 2026-09-25 06:14:28 UTC

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

(339428709/4, 4603432824371/8)
(5775132654/49, 375485951983141/343)
(157598709/4, 71410989371/8)
(2276968046, 108601556659612)
(7511241, 304719659722)

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 06:14:28 UTC · history

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