Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #4504

y² = x³ + x² − 1201503305x + 16022243175799

a-invariants: [0, 1, 0, -1201503305, 16022243175799]
c-invariants: [57672158656, -13843564136842240]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
conductor (N): 302719655002017728
discriminant (Δ): 102907071682036630136655872
Faltings height: 3.9406
naive height: 74.3341
primes of bad reduction: 2, 41, 73, 113, 353, 367, 2633
regulator: 86957.6948786523649952084669952322990113676236955123598
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:32:47 UTC
last updated: 2026-10-17 10:32:47 UTC

Witness: 8 independent points log in to add more points →

(-9731, 5176168)
(5890, 3024857)
(19657, 9884)
(21097, 253964)
(23187, 793544)
(-629, 4096064)
(95925/4, 8003569/8)
(20730, 154507)

Commentary

BASE torsion/torsion_Z2.tsv.gz:635333 + Werr Core & 4-Pillar Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:32:47 UTC · history

Log in to edit commentary.