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curve #779

y² + xy + y = x³ − x² − 3391172427x + 83084924109915

a-invariants: [1, -1, 1, -3391172427, 83084924109915]
rank (lower bound): ≥ 11
torsion subgroup: trivial
conductor (N): 31433524696380244247818
discriminant (Δ): -486166483982466262137900105728
Faltings height: 4.4334
naive height: 77.6249
primes of bad reduction: 2, 59, 5669, 876181, 53630369159
regulator: 2645630.72327408283575367116298357864499311819188923757652167
submitted by: Michael Rubinstein
submitted at: 2026-09-18 12:38:41 UTC
last updated: 2026-09-18 12:38:41 UTC

Witness: 11 independent points log in to add more points →

(37227, 2885130)
(46667, -5167190)
(-64725, -5573110)
(133515, -44903926)
(-15637, 11509514)
(71211, -14273014)
(-64253, 6007882)
(-45845, -11901686)
(-60949, -7929334)
(34395, 2653850)
(16223, 5678662)

Commentary

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

last edited by Michael Rubinstein at 2026-09-18 12:38:42 UTC · history

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