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curve #1315

y² + xy = x³ − x² − 4058145576x + 99508012617636

a-invariants: [1, -1, 0, -4058145576, 99508012617636]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/3ℤ
conductor (N): 16312174335162
discriminant (Δ): -277303359322162277284937076
Faltings height: 4.1604
naive height: 77.9856
primes of bad reduction: 2, 3, 23, 29, 31, 37, 47, 271
regulator: 753.47826477252193339000754291068855649042492381239
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:30:46 UTC
last updated: 2026-09-24 17:30:46 UTC

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

(36774, 38436)
(33954, 911226)
(41145, 1459011)
(38014, 397230)
(37456, 213710)
(39406, 864884)

Commentary

Torsion Z/3. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-24 17:30:46 UTC · history

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