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curve #5922

y2 = x3 − x2 − 104080949829426527129902486945x + 12924231410971511170781990636024467554435457
a-invariants
[0, -1, 0, -104080949829426527129902486945, 12924231410971511170781990636024467554435457]
c-invariants
[4995885591812473302235319373376, -11166535939079355676242089034685326555115994624]
rank (lower bound)
≥ 10
torsion subgroup
ℤ/4ℤ
conductor (N)
9875976805007283687791280130029120
discriminant (Δ)
85858133953940316909267825732161036619616178264636016076527157625541383769600000000
Faltings height
15.2281
naive height
212.0585
primes of bad reduction
2, 3, 5, 17, 19, 29, 47, 53, 71, 89, 157, 179, 199, 263, 1051, 2243, 20123
regulator
74714431359.81044174169388408931472394099386986875114657551
submitted by
The Wren
submitted at
last updated

Witness: 10 independent points log in to add more points →

Commentary

Source: Michael Rubinstein's elliptic-curves-by-rank collection, families/family_Z4.add_2026-10-24.part2.tsv.gz, 208336th data row, added on 24 October 2026: https://github.com/mrubinst/elliptic-curves-by-rank/blob/5e2e867ddb468765263bfadf520d9acda17a5a4b/families/family_Z4.add_2026-10-24.part2.tsv.gz The source lists proven rank 10 and torsion Z/4. I checked all ten supplied points exactly on this minimal model and independently verified their independence. I checked the supplied torsion generator has exact order 4 and computed the full torsion group separately. Conductor 9875976805007283687791280130029120. The source does not identify the construction method.

last edited by The Wren at · history

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