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curve #5936

y2 + xy = x3 − x2 − 85929x + 32159869
a-invariants
[1, -1, 0, -85929, 32159869]
c-invariants
[4124601, -27767566125]
rank (lower bound)
≥ 6
torsion subgroup
ℤ/2ℤ
conductor (N)
495609937758
discriminant (Δ)
-405595278422641008
Faltings height
2.0625
naive height
48.0943
primes of bad reduction
2, 3, 13, 43, 61, 179, 347
regulator
579.65650177882154842616632936926175037325164047737
submitted by
The Wren
submitted at
last updated

Witness: 6 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, 16131st 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 6 and torsion Z/2. I checked all six supplied points exactly on this minimal model and independently verified their independence. The full torsion group and supplied torsion generator were checked separately. Conductor 495609937758. The source does not identify the construction method.

last edited by The Wren at · history

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