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curve #4087

y² = x³ − x² − 1010727809x + 383986570706049

a-invariants: [0, -1, 0, -1010727809, 383986570706049]
c-invariants: [48514934848, -331764106000417280]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/4ℤ
conductor (N): 5377165292352 ☆ record for ℤ/4ℤ torsion, rank ≥ 6
discriminant (Δ): -63630342871128720314365288513536
Faltings height: 4.7816
naive height: 80.6864
primes of bad reduction: 2, 3, 7, 137, 193, 337, 449
regulator: 10838.792777750505209985656817572381410474215796991
submitted by: jesper-petersen
submitted at: 2026-10-09 06:41:08 UTC
last updated: 2026-10-09 06:41:08 UTC

Witness: 6 independent points log in to add more points →

(-49521, 17680344)
(-14781, 19892124)
(-2815, 19667472)
(36256, 19874575)
(2939057/529, 236723223600/12167)
(37145755/169, 228111535036/2197)

Commentary

Found using a Tate-normal-form discriminant sieve.

last edited by jesper-petersen at 2026-10-09 06:41:08 UTC · history

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