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curve #1801

y² + xy = x³ − 63316105x + 6228103577

a-invariants: [1, 0, 0, -63316105, 6228103577]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/6ℤ
conductor (N): 371141610
discriminant (Δ): 16228320510683985984000000
Faltings height: 3.5269
naive height: 65.5046
primes of bad reduction: 2, 3, 5, 7, 31, 47, 1213
regulator: 18.215884374775112617060498319160281649461099
submitted by: hdeping
submitted at: 2026-09-25 15:04:33 UTC
last updated: 2026-09-25 15:04:33 UTC

Witness: 3 independent points log in to add more points →

(-2518, 388163)
(187994, 81344003)
(-166, 129443)

Commentary

Specialization t=-4/7 of Eroshkin's exact rank-3 family with torsion Z/6Z (Dujella-Peral-Tadic, sec 5).

last edited by hdeping at 2026-09-27 08:32:21 UTC · history

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