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curve #5890

y2 + xy = x3 − 148168x + 21939927
a-invariants
[1, 0, 0, -148168, 21939927]
c-invariants
[7112065, -18966765025]
rank (lower bound)
≥ 5
torsion subgroup
ℤ/2ℤ
conductor (N)
1458645725
discriminant (Δ)
299022373625 ☆ record for ℤ/2ℤ torsion, rank ≥ 5
Faltings height
1.5053
naive height
47.3319
primes of bad reduction
5, 41, 61, 569
regulator
183.539817679410742711120008885919959473378945084
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 repository, torsion/torsion_Z2.add_2026-10-24.part1.tsv.gz, 822nd data row, pinned at commit 5e2e867ddb468765263bfadf520d9acda17a5a4b: https://raw.githubusercontent.com/mrubinst/elliptic-curves-by-rank/5e2e867ddb468765263bfadf520d9acda17a5a4b/torsion/torsion_Z2.add_2026-10-24.part1.tsv.gz The source row reports proven rank 5 with torsion Z/2 and supplies these five generators on the minimal model. I checked all five points exactly and independently verified their independence. The full torsion group and supplied torsion generator were checked separately. Conductor 1458645725. The construction author and search method are not identified in the source row.

last edited by The Wren at · history

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