curve #1615

y² + xy = x³ − 1707486852180981621732968420x − 17216215758728072194697189293040377167600

a-invariants: [1, 0, 0, -1707486852180981621732968420, -17216215758728072194697189293040377167600]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 10653519586931119470
discriminant (Δ): 190560654339073620935572242783982607067139442478388938178243220139854021001216000000
Faltings height: 14.6816
naive height: 199.7281
primes of bad reduction: 2, 3, 5, 11, 13, 23, 31, 199, 409, 4729, 9049
regulator: 9553.539061890237756573804545075037780075153003
submitted by: Michael Rubinstein
submitted at: 2026-09-25 01:38:07 UTC
last updated: 2026-09-25 01:38:07 UTC

(-17130074877560, 83704977705322388380)
(45737732696440, 19178307137128268380)
(59532139111240, 303512474592782012380)
(7050269797405926358600/129800449, 331618023454276743311087512030940/1478816515457)

Torsion Z/6+Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 01:38:07 UTC · history