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curve #1461

y² + xy = x³ − 164077875x + 823376390625

a-invariants: [1, 0, 0, -164077875, 823376390625]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/7ℤ
conductor (N): 4520130
discriminant (Δ): -10180801072375568640000000
Faltings height: 3.5896
naive height: 68.3965
primes of bad reduction: 2, 3, 5, 17, 8863
regulator: 7.98212881788585275058936599926346007733563
submitted by: Michael Rubinstein
submitted at: 2026-09-25 00:05:19 UTC
last updated: 2026-09-25 00:05:19 UTC

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

(528750/169, 1278856125/2197)
(185250, -79639875)

Commentary

Torsion Z/7. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 00:05:19 UTC · history

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