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curve #1470

y² + xy = x³ + 563011x + 17346765810

a-invariants: [1, 0, 0, 563011, 17346765810]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/8ℤ
conductor (N): 503139
discriminant (Δ): -130003961230859961434553
Faltings height: 3.1141
naive height: 60.6765
primes of bad reduction: 3, 7, 13, 19, 97
regulator: 15.4115651935179965766847048813205150190217
submitted by: Michael Rubinstein
submitted at: 2026-09-25 00:14:18 UTC
last updated: 2026-09-25 00:14:18 UTC

Witness: 2 independent points log in to add more points →

(-2483, 26578)
(113227, 38044495)

Commentary

Torsion Z/8. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 00:14:19 UTC · history

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