Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #1251

y² + y = x³ + x² − 2627151804331940x + 51831310381902842183300

a-invariants: [0, 1, 1, -2627151804331940, 51831310381902842183300]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/5ℤ
conductor (N): 4832263166746443
discriminant (Δ): -87273706811585089066758879277976356877886123
Faltings height: 7.5099
naive height: 118.1277
primes of bad reduction: 3, 29, 227, 587, 9829, 42409
regulator: 506.56841691591444273654867200585198200094094
submitted by: hdeping
submitted at: 2026-09-24 16:26:52 UTC
last updated: 2026-09-24 16:26:52 UTC

Witness: 3 independent points log in to add more points →

(30418000, 7937626699)
(-20580472625/361, 876167423962816/6859)
(104695823614/11881, 221919085790683240/1295029)

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=17023/681.

last edited by hdeping at 2026-09-27 08:32:53 UTC · history

Log in to edit commentary.