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curve #3537

y² + xy + y = x³ − 1929362430154x + 1030679501754687356

a-invariants: [1, 0, 1, -1929362430154, 1030679501754687356]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/6ℤ
conductor (N): 591998388510 ☆ record for ℤ/6ℤ torsion, rank ≥ 5
discriminant (Δ): 729976059823193322304960882390593600
Faltings height: 5.8049
naive height: 96.4782
primes of bad reduction: 2, 3, 5, 23, 31, 103, 167, 1609
regulator: 670.294282193583128863884473074491706261221517418
submitted by: Tom Fisher
submitted at: 2026-09-27 23:26:13 UTC
last updated: 2026-09-27 23:26:13 UTC

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

(782668, 7838468)
(782944, 6136307)
(840421, 52481537)
(106093, 909442313)
(73572838, 630919706408)

Commentary

2-isogenous to curve#3490

last edited by Tom Fisher at 2026-09-27 23:59:45 UTC · history

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