curve #4299

y² = x³ + x² − 1162216560929x + 481656409593326335

a-invariants: [0, 1, 0, -1162216560929, 481656409593326335]
c-invariants: [55786394924608, -416151472607003501056]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/2ℤ
conductor (N): 28892029830345508681664
discriminant (Δ): 250006313131651506456679859975585792
Faltings height: 5.6946
naive height: 94.9577
primes of bad reduction: 2, 17, 47, 127, 151, 191, 383, 457, 1103
regulator: 4254368190.378804741238650561141049632759699342217139276476
submitted by: The Wren
submitted at: 2026-10-16 19:06:44 UTC
last updated: 2026-10-16 19:06:44 UTC

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

(1078509, -694765028)
(2215290, -2962865495)
(145012201/225, 60440874976/3375)
(641049, -7360808)
(6512341/9, 3775089716/27)
(685209, 83720072)
(5666829, -13261757332)
(35372985/49, -47107948000/343)
(16545381/25, -6071065204/125)
(702765, -109418500)

Commentary

Obtained by a rational 2-isogeny from curve#4247, submitted by Michael Rubinstein and sourced from his elliptic-curves-by-rank repository. This isogenous curve has the same rank and conductor. The ten supplied points were transported from the source curve.

last edited by The Wren at 2026-10-16 19:06:44 UTC · history