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curve #5932

y2 + xy = x3 + x2 − 688444467x + 6950135008665
a-invariants
[1, 1, 0, -688444467, 6950135008665]
c-invariants
[33045334441, -6005164487494805]
rank (lower bound)
≥ 8
torsion subgroup
ℤ/2ℤ
conductor (N)
221459249378724918
discriminant (Δ)
13489962958715165808204132
Faltings height
3.7890
naive height
72.6634
primes of bad reduction
2, 3, 11, 47, 73, 89, 97, 269, 353, 1193
regulator
31369.7941744886517067034740994896531842071136811932828
submitted by
The Wren
submitted at
last updated

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

Commentary

Source: Michael Rubinstein's elliptic-curves-by-rank collection, torsion/torsion_Z2.add_2026-10-24.part3.tsv.gz, 484140th 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 221459249378724918. The source does not identify the construction method.

last edited by The Wren at · history

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