curve #247

y² = x³ + x² − 482829160x + 4083394233624

a-invariants: [0, 1, 0, -482829160, 4083394233624]
rank (lower bound): ≥ 7
conductor (N): 53804918203167712
naive height: 71.5991
Faltings height: 3.4954
discriminant (Δ): -2573166408148292658688
primes of bad reduction: 2, 7, 23, 61, 42023, 582011
regulator: 10410.85435838384587885146965481704905169934041329564
submitted by: Warricker-hash
submitted at: 2026-07-18 10:36:02 UTC
last updated: 2026-07-18 10:36:02 UTC

Witness: 7 independent points

(770837854/81, -21401460733402/729)
(1219424009797779/65401413169, 20911576833713426134638/16725561199600553)
(50669/4, -30043/8)
(12248926/961, 350032214/29791)
(3243689/256, 12744683/4096)
(1304718224057366/102840151969, 28698223219897682746/32979499814482703)
(11391, -248304)

Commentary

"I have also generated a supplementary dataset of 250+ rank 6 curves from this exact same family with massive conductors. Would you like me to include them also?" -- Hm... if they have huge conductor then probably not. If you'd like to chat about this, please join the ICARM Zulip: https://icarm.zulipchat.com/#narrow/channel/519875-general/topic/requesting.20access.20to.20this.20zulip/with/573899865 We have a channel here: https://icarm.zulipchat.com/#narrow/channel/519875-general/topic/Elliptic.20Curve.20Rank.20Leaderboard/with/608813888

last edited by David Renshaw at 2026-07-21 11:34:36 UTC · history