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curve #1610

y² + xy + y = x³ − 60694409144x + 5849551333071542

a-invariants: [1, 0, 1, -60694409144, 5849551333071542]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/6ℤ
conductor (N): 3637272210
discriminant (Δ): -472325886415978832675179413500400
Faltings height: 5.0638
naive height: 86.1334
primes of bad reduction: 2, 3, 5, 11, 13, 23, 191, 193
regulator: 64.77021721277704136819405362812158091096843604
submitted by: Michael Rubinstein
submitted at: 2026-09-25 01:32:59 UTC
last updated: 2026-09-25 01:32:59 UTC

Witness: 4 independent points log in to add more points →

(-165759, 106646479)
(121281, 16444159)
(588279/4, 81110477/8)
(1029045, 1015892323)

Commentary

Torsion Z/6. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 01:32:59 UTC · history

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