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curve #3508

y² = x³ − x² − 25149767425x − 167124429071039

a-invariants: [0, -1, 0, -25149767425, -167124429071039]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 55660539421203992256
discriminant (Δ): 1006012752543837660751945087352832
Faltings height: 5.0223
naive height: 83.4579
primes of bad reduction: 2, 3, 41, 73, 97, 113, 127, 353, 439, 449
regulator: 556318.06665186967247112585389200582485938896117824822468
submitted by: Michael Rubinstein
submitted at: 2026-09-27 12:46:09 UTC
last updated: 2026-09-27 12:46:09 UTC

Witness: 9 independent points log in to add more points →

(-6671, 593928)
(-89599, 36972456)
(-53679, 32065784)
(434833, 266673672)
(47894905/121, -303207965064/1331)
(-48719, 30700296)
(-122157, -32897012)
(-325619/4, 292928049/8)
(240865, 88029144)

Commentary

Torsion Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-27 12:46:09 UTC · history

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