Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #1255

y² + y = x³ − x² − 8180435782450x + 9005465481752090182

a-invariants: [0, -1, 1, -8180435782450, 9005465481752090182]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/5ℤ
conductor (N): 9855597593317
discriminant (Δ): 1087248168054702165148130422712938357
Faltings height: 6.0415
naive height: 100.8119
primes of bad reduction: 7, 17, 29, 167, 17101001
regulator: 11799.36492683898883380181970124519055258608032
submitted by: hdeping
submitted at: 2026-09-24 16:29:07 UTC
last updated: 2026-09-24 16:29:07 UTC

Witness: 4 independent points log in to add more points →

(637468241/361, 1766746769652/6859)
(239140680496/139129, 7829618012476473/51895117)
(-197937676/169, 9053122770297/2197)
(122354509556854/61230625, 382689241163933961317/479129640625)

Commentary

Found by a Mestre-Nagao sieve over the Tate normal form family y^2+(t+1)xy+ty=x^3+tx^2 with torsion Z/5Z, at t=33901/-833.

last edited by hdeping at 2026-09-27 08:29:25 UTC · history

Log in to edit commentary.