curve #158

y² + y = x³ − x² − 1876573260x + 32705933898332

a-invariants: [0, -1, 1, -1876573260, 32705933898332]
rank (lower bound): ≥ 13
conductor (N): 13048475524065056885495472921 ★ record for rank ≥ 13
naive height: 75.7603 ★ record for rank ≥ 13
Faltings height: 4.2452 ★ record for rank ≥ 13
discriminant (Δ): -39145426572195170656486418763 ★ record for rank ≥ 13
primes of bad reduction: 3, 4349491841355018961831824307
regulator: 740620279.4326354740651118477378116431858161004526275963581006162
submitted by: Andrew Sutherland
last updated: 2026-07-01 22:44:39

Witness: 13 independent points

(7741928124496/345030625, 8823560993548208669/6408943859375)
(132552615/3481, -833270007898/205379)
(1625667815/63001, 19131107316838/15813251)
(15572079543/398161, 1098982569620230/251239591)
(419003945245/34082244, -674555808769168789/198972140472)
(181207744936/4566769, 44420007350544652/9759185353)
(43390, 5741911)
(937218533/21316, -18462206221191/3112136)
(426410835/19321, -3835378260566/2685619)
(97096629/6889, 1720725812756/571787)
(559519/25, -173060047/125)
(784478154/14641, -16426944244376/1771561)
(-965919/25, 861795179/125)

Commentary

Found by Noam D. Elkies in June 2026, using an improved version of the methods described in his JMM 2023 talk https://abel.math.harvard.edu/~elkies/Elkies_JMM23.pdf

last edited by Andrew Sutherland at 2026-06-24 23:46:15 · history