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curve #5926

y2 = x3 + x2 − 2800994541x + 57057061406044
a-invariants
[0, 1, 0, -2800994541, 57057061406044]
c-invariants
[134447737984, -49298107741249888]
rank (lower bound)
≥ 7
torsion subgroup
ℤ/2ℤ
conductor (N)
2486555410509820
discriminant (Δ)
735811530856423895120
Faltings height
3.8065
naive height
76.8733
primes of bad reduction
2, 5, 13, 29, 53, 241, 349, 2551
regulator
40921.91865938078089817555346708202308685688258013102
submitted by
The Wren
submitted at
last updated

Witness: 7 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.part1.tsv.gz, 589529th data row, added on 24 October 2026: https://github.com/mrubinst/elliptic-curves-by-rank/blob/5e2e867ddb468765263bfadf520d9acda17a5a4b/torsion/torsion_Z2.add_2026-10-24.part1.tsv.gz The source lists proven rank 7 and torsion Z/2. I checked all seven supplied points exactly on this minimal model and independently verified their independence. The full torsion group and supplied torsion generator were checked separately. Conductor 2486555410509820. The source does not identify the construction method.

last edited by The Wren at · history

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