Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #5673

y² = x³ − 27501222402x

a-invariants: [0, 0, 0, -27501222402, 0]
c-invariants: [1320058675296, 0]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 5378255883408118397184
discriminant (Δ): 1331177500660244811959744590643712
Faltings height: 5.0454
naive height: 83.7261
primes of bad reduction: 2, 3, 19, 41, 67, 73, 401
regulator: 980655.058406497618368442525299518334840424746504378223
submitted by: Michael Rubinstein
submitted at: 2026-10-24 04:21:13 UTC
last updated: 2026-10-24 04:21:13 UTC

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

(-52193, 35960977)
(-26937, 26856189)
(-91656, 41840964)
(-6690888/121, 48933809388/1331)
(-142721, 31904191)
(-162729, 12886587)
(213282, 61939602)
(8455266/49, 6795215442/343)

Commentary

Rank 8, proved: 8 independent points listed, matching the 2-descent upper bound. Torsion Z/2. Member of the family y^2 = x^3 + a x.

last edited by Michael Rubinstein at 2026-10-24 04:21:13 UTC · history

Log in to edit commentary.