curve #3350

y² + xy + y = x³ + 7484034194592x + 12165299389649646556

a-invariants: [1, 0, 1, 7484034194592, 12165299389649646556]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/6ℤ
conductor (N): 50250886947030
discriminant (Δ): -90761557543449764403602874373201302135750
Faltings height: 6.5436
naive height: 101.4134
primes of bad reduction: 2, 3, 5, 7, 11, 23, 29, 31, 89, 11821
regulator: 8865.37630213462261892750112107141287426455487066
submitted by: David Renshaw
submitted at: 2026-09-26 21:09:36 UTC
last updated: 2026-09-26 21:09:36 UTC

Witness: 5 independent points log in to add more points →

(2289170, 6424854417)
(721637345/64, 20024863442229/512)
(-864950605/676, -12349881626913/17576)
(-1524795128/1521, 113437476920756/59319)
(-3930121/4, -15720717843/8)

Commentary

Rationally isogenous to curve#1670 (isogeny class computed with PARI/GP ellisomat; global minimal model). The witnesses are the images of that curve's witnesses under the isogeny, so they remain independent and the rank bound 5 carries over. Torsion ℤ/6ℤ.

last edited by David Renshaw at 2026-09-26 21:09:36 UTC · history