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curve #1340

y² + xy = x³ − x² − 3507651369384x + 2528175831282687140

a-invariants: [1, -1, 0, -3507651369384, 2528175831282687140]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/3ℤ
conductor (N): 33742365235013610
discriminant (Δ): 834555502253538549546430296304687500
Faltings height: 5.8980
naive height: 98.2715
primes of bad reduction: 2, 3, 5, 7, 17, 23, 37, 4783, 5059
regulator: 3947.671028097308241175251168435050697337318324926419
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:35:02 UTC
last updated: 2026-09-24 17:35:02 UTC

Witness: 7 independent points log in to add more points →

(1617376, 1041249322)
(-1156514, -2243961068)
(-1924064, 1468678282)
(5007686, -10516317468)
(970135, 195305335)
(10053424/9, 1651068614/27)
(11788306, 39985740292)

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 17:35:03 UTC · history

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