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curve #5939

y2 + xy = x3 − x2 − 38418x + 2199680
a-invariants
[1, -1, 0, -38418, 2199680]
c-invariants
[1844073, -1892225205]
rank (lower bound)
≥ 5
torsion subgroup
ℤ/2ℤ
conductor (N)
6596389746
discriminant (Δ)
1556972257307364
Faltings height
1.6254
naive height
43.2825
primes of bad reduction
2, 3, 31, 47, 97, 2593
regulator
78.6156485633798451008646416822779483018688186708
submitted by
The Wren
submitted at
last updated

Witness: 5 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, 846th 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 5 and torsion Z/2. I checked all five supplied points exactly on this minimal model and independently verified their independence. The full torsion group and supplied torsion generator were checked separately. Conductor 6596389746. The source does not identify the construction method.

last edited by The Wren at · history

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