curve #1453

y² + xy + y = x³ − 3851792636729604242492843x + 2909660917706747033230507914830666306

a-invariants: [1, 0, 1, -3851792636729604242492843, 2909660917706747033230507914830666306]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 316220244452970
discriminant (Δ): 1361137936235986858125824536219446431653498884409420251846313476562500
Faltings height: 12.6501
naive height: 181.4453
primes of bad reduction: 2, 3, 5, 11, 13, 31, 47, 137, 179, 2063
regulator: 187.118745782382211384496510825246239335156
submitted by: Michael Rubinstein
submitted at: 2026-09-24 23:57:19 UTC
last updated: 2026-09-24 23:57:19 UTC

(221793473819495/196, 7350663297126676983/2744)
(57264290938762833931035/50315424721, 103768828805314348671850086757942/11286303234592231)

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 2026-09-24 23:57:19 UTC · history