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curve #3507

y² = x³ + x² + 130197089055x + 19824343466561599

a-invariants: [0, 1, 0, 130197089055, 19824343466561599]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 45709648312790275648
discriminant (Δ): -311025725811552872241096218944503808
Faltings height: 5.4964
naive height: 88.5745
primes of bad reduction: 2, 17, 89, 223, 257, 271, 433, 4129
regulator: 887310.91995562667186740864148686838490193838425230140558
submitted by: Michael Rubinstein
submitted at: 2026-09-27 12:45:58 UTC
last updated: 2026-09-27 12:45:58 UTC

Witness: 9 independent points log in to add more points →

(-63654, 106202009)
(3441867, 6421982344)
(-1064237/9, -1422390952/27)
(-56773, 110678264)
(601115, -561510968)
(146925, -205244332)
(-5823541/49, -17730223288/343)
(16852859, 69200751752)
(1647515, 2169375032)

Commentary

Torsion Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-27 12:45:58 UTC · history

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