Elliptic Curve Rank Leaderboard

curve #277

y2 = x3 − 606045924x + 5289852801024
a-invariants
[0, 0, 0, -606045924, 5289852801024]
rank (lower bound)
≥ 6
torsion subgroup
trivial
conductor (N)
28428075513538468416
naive height
72.2810
Faltings height
3.9853
discriminant (Δ)
2157660911429827456151752704
primes of bad reduction
2, 3, 11, 1216681, 335245441
regulator
4975.3262359149538714498786181623068386819786827935
submitted by
Daksh Shami
submitted at
2026-08-21 19:52:52 UTC
last updated
2026-08-21 19:52:52 UTC

Witness: 6 independent points

Commentary

Rank >= 6. Found during a preliminary search among rational specializations of the classical one-parameter family y^2 = x^3 - u^2*x + 1, at u = 373/264. The six displayed rational points were certified independent modulo torsion by the ICARM exact 2-descent verifier (descent matrix rank 6), establishing rank E(Q) >= 6. Candidate search and the computational verification workflow were carried out with assistance from OpenAI Codex using GPT-5.6 Sol, together with exact computations in SageMath.

last edited by Daksh Shami at 2026-08-21 19:52:53 UTC · history

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