curve #244

y² = x³ − 44788551847x + 2462203786988170

a-invariants: [0, 0, 0, -44788551847, 2462203786988170]
rank (lower bound): ≥ 14
torsion subgroup: trivial
conductor (N): 97849916723105200970396784134696 ★ record for rank ≥ 14
naive height: 85.1893 ★ record for rank ≥ 14
Faltings height: 5.1313 ★ record for rank ≥ 14
discriminant (Δ): 3131197335139366431052697092310272 ★ record for rank ≥ 14
primes of bad reduction: 2, 19937, 100585774481, 6099217213561621
regulator: 14021721492.1716638850528837824332581766485430502825171168406532475
submitted by: Andrew Sutherland
submitted at: 2026-07-06 21:36:14 UTC
last updated: 2026-07-06 21:36:14 UTC

Witness: 14 independent points

(-15631379015/99856, -2369204678362285/31554496)
(4052355557/3481, -253871365077038/205379)
(5262768921/196, 381775442683333/2744)
(-222001919/1764, 5789112700393/74088)
(1393321, 1626336962)
(-9695799134155739/91418546025, 2144515602814138618661134/27640854483388875)
(5612388061/15625, 353280062993066/1953125)
(180414, -15939116)
(8914742837/39601, -485001428074178/7880599)
(73674598589/167281, -17863087725156374/68417929)
(34408221678887385/1335975352336, -56224932570097492293210595/1544179095145451584)
(790421, 678887362)
(337343392162/142129, 195171010842841522/53582633)
(98575401/4, -978671293277/8)

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 2026-07-06 21:37:24 UTC · history