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curve #3437

y² + xy + y = x³ − 16785799414680x + 26477982529328587642

a-invariants: [1, 0, 1, -16785799414680, 26477982529328587642]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/3ℤ
conductor (N): 3049169315882817126 ☆ record for ℤ/3ℤ torsion, rank ≥ 8
discriminant (Δ): -172561986650132937440990832445220816676
Faltings height: 6.3103
naive height: 102.9688
primes of bad reduction: 2, 3, 61, 67, 73, 149, 271, 307, 313, 439
regulator: 179211.388190574160445515899246918814256483641414614043
submitted by: Michael Rubinstein
submitted at: 2026-09-27 05:33:28 UTC
last updated: 2026-09-27 05:33:28 UTC

Witness: 8 independent points log in to add more points →

(2593187, 621167445)
(2682392, -868698783)
(8714852, 23278113405)
(480343985/64, -9207631871829/512)
(2458817, 263806965)
(2330351, 126247257)
(376735577/121, 2789067617595/1331)
(765541466/289, 3801238377003/4913)

Commentary

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

last edited by Michael Rubinstein at 2026-09-27 05:33:28 UTC · history

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