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curve #1368

y² = x³ − x² − 25626590985x + 518606218271241

a-invariants: [0, -1, 0, -25626590985, 518606218271241]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 1643831925364091722944
discriminant (Δ): 960907607489839771685555219238912
Faltings height: 5.0209
naive height: 83.5143
primes of bad reduction: 2, 3, 23, 41, 73, 113, 257, 809, 1783, 2969
regulator: 981799.41263873871966193456384841898983390765585368199413
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:39:54 UTC
last updated: 2026-09-24 17:39:54 UTC

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

(280895, -124432004)
(-11517, -28499472)
(198877, -57341280)
(185331, 46204344)
(-166551, -12911832)
(9782459/25, 28063606952/125)
(64778621/289, -381701159584/4913)
(-107419/4, 275673331/8)
(16961, -9425104)

Commentary

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

last edited by Michael Rubinstein at 2026-09-24 17:39:54 UTC · history

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