curve #3947

y² = x³ − x² − 837468815739430x + 9326761552687403763400

a-invariants: [0, -1, 0, -837468815739430, 9326761552687403763400]
c-invariants: [40198503155492656, -8058321740330897918621696]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 1578385609386038880
discriminant (Δ): 12154003312299691040575162140484282726440000
Faltings height: 7.2691
naive height: 114.6978
primes of bad reduction: 2, 3, 5, 7, 19, 31, 71, 101, 157, 281, 2521
regulator: 1461300336.979617524468990498949013244194569757018608
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:32:02 UTC
last updated: 2026-10-05 04:32:02 UTC

Witness: 7 independent points log in to add more points →

(8234668060609/242064, 16929025198893108665/119095488)
(190034506408579247585/7737320812816, -1286604861921347953943453282775/21522162522212236864)
(38312339447761/774400, -203288298101368825959/681472000)
(66024521799049/2304, -536485113054454277285/110592)
(2923306409/64, -131905178915445/512)
(16646719126409/984064, 802785972336439845/976191488)
(12359688203502259/375003225, 961420372410930264561248/7261937452125)

Commentary

Unlisted rational-isogeny neighbor of curve#3664 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 7: 7 independent points certified by the unchanged ICARM verifier, with a matching unconditional upper bound computed using PARI/GP 2.17.2 ellrank. This is an additional representative of a known isogeny class, not a claim of a new world rank record.

last edited by Odbayar Shinebayar at 2026-10-05 04:32:02 UTC · history