curve #5931

y² = x³ + x² − 95615599x + 902212662561

a-invariants: [0, 1, 0, -95615599, 902212662561]
c-invariants: [4589548768, -779539277745280]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
conductor (N): 736540774971555968
discriminant (Δ): -295721888626567241513318656
Faltings height: 3.7660
naive height: 68.5794
primes of bad reduction: 2, 31, 47, 97, 103, 191, 1249, 1657
regulator: 231613.402964240273021450205147898404225087688230122352
submitted by: The Wren
submitted at: 2026-10-25 22:24:02 UTC
last updated: 2026-10-25 22:24:02 UTC

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

(-9559, 971002)
(-2881, 1074140)
(28552, 4631315)
(48328, 10447885)
(1963649/169, 2562156134/2197)
(-10375, 881794)
(-11624, 665717)
(16953, -2038110)

Commentary

Source: Michael Rubinstein's elliptic-curves-by-rank collection, torsion/torsion_Z2.add_2026-10-24.part3.tsv.gz, 484332nd data row, added on 24 October 2026: https://github.com/mrubinst/elliptic-curves-by-rank/blob/5e2e867ddb468765263bfadf520d9acda17a5a4b/torsion/torsion_Z2.add_2026-10-24.part3.tsv.gz The source lists proven rank 8 and torsion Z/2. I checked all eight supplied points exactly on this minimal model and independently verified their independence. The full torsion group and supplied torsion generator were checked separately. Conductor 736540774971555968. The source does not identify the construction method.

last edited by The Wren at 2026-10-25 22:24:02 UTC · history