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curve #1651

y² + xy + y = x³ + x² − 37770966938x + 3086279763130406

a-invariants: [1, 1, 1, -37770966938, 3086279763130406]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/4ℤ
conductor (N): 379817931075
discriminant (Δ): -666204012562703260503406794609375
Faltings height: 5.0355
naive height: 84.8546
primes of bad reduction: 3, 5, 11, 19, 31, 71, 101, 109
regulator: 1093.41499423393443112471886957744429953643044436
submitted by: Michael Rubinstein
submitted at: 2026-09-25 02:26:23 UTC
last updated: 2026-09-25 02:26:23 UTC

Witness: 5 independent points log in to add more points →

(41434, 39884327)
(938935/9, -454231616/27)
(488834295/1156, 9835754849383/39304)
(21139731/196, -44997853333/2744)
(145284, 25721977)

Commentary

Torsion Z/4. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 02:26:23 UTC · history

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