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curve #5937

y2 + xy = x3 + x2 − 267451x + 31618249
a-invariants
[1, 1, 0, -267451, 31618249]
c-invariants
[12837673, -27414449621]
rank (lower bound)
≥ 6
torsion subgroup
ℤ/2ℤ
conductor (N)
2468994518802
discriminant (Δ)
789451121408864292
Faltings height
2.1340
naive height
49.1037
primes of bad reduction
2, 3, 7, 23, 193, 331, 40009
regulator
692.91154680927603859348216472349607403974603934278
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, 16418th 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 2468994518802. The source does not identify the construction method.

last edited by The Wren at · history

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