Elliptic Curve Rank Leaderboard

← home  ·  all curves  ·  JSON ↓

curve #6082

y2 = x3 − 13869102100000325196x + 58311658014030883749376750480
a-invariants
[0, 0, 0, -13869102100000325196, 58311658014030883749376750480]
c-invariants
[665716900800015609408, -50381272524122683559461512414720]
rank (lower bound)
≥ 9
torsion subgroup
ℤ/4ℤ
conductor (N)
1056738254468057369589312 ☆ record for ℤ/4ℤ torsion, rank ≥ 9
discriminant (Δ)
-1298171803292146613206686492839395684712914189356048219242496 ☆ record for ℤ/4ℤ torsion, rank ≥ 9
Faltings height
10.2196 ☆ record for ℤ/4ℤ torsion, rank ≥ 9
naive height
145.9943 ☆ record for ℤ/4ℤ torsion, rank ≥ 9
primes of bad reduction
2, 3, 23, 47, 59, 131, 347, 491, 11329, 113761
regulator
25166164.936434741884778183641842112708218391248323990300
submitted by
The Wren
submitted at
last updated

Witness: 9 independent points log in to add more points →

Commentary

Original search by mpjunior92 (2026), public Yukon elliptic-rank challenge submission f9dcdb3a-2049-49d5-94bb-cc04dc429991. Source: https://raw.githubusercontent.com/Layr-Labs/elliptic-rank-challenge-public/098b17019380774646df844473bf6a59f257e748/submission/board/4-9b.ec . The source used a Mestre-Nagao sieve in the Kubert Z/4 family y^2 + x*y - t*y = x^3 - t*x^2 with t=u/(D*s^2), (D,s,u)=(6,8648,-1316843833). The nine supplied points have been checked exactly on the minimal model and certified independent modulo torsion by an exact rank-9 F_5 reduction matrix at nine good primes.

last edited by The Wren at · history

Log in to edit commentary.