curve #1938

y² + xy + y = x³ − 2557499874808783579775134722531513x + 49997987268990292225606516653085266862246125287656

a-invariants: [1, 0, 1, -2557499874808783579775134722531513, 49997987268990292225606516653085266862246125287656]
rank (lower bound): ≥ 13
torsion subgroup: ℤ/3ℤ
conductor (N): 623233714131363083533304034631437428047196010
discriminant (Δ): -9314041989928374944851336723423729245175533779994688994175929139290469421275907740315451340835937500 ☆ record for ℤ/3ℤ torsion, rank ≥ 13
Faltings height: 18.0294 ☆ record for ℤ/3ℤ torsion, rank ≥ 13
naive height: 242.3953 ☆ record for ℤ/3ℤ torsion, rank ≥ 13
primes of bad reduction: 2, 3, 5, 17, 19, 29, 31, 43, 53, 59, 67, 79, 1667, 50359, 67531, 69463, 122903239
regulator: 151348112410.5234422594250886590959504525811978559513744413365906
submitted by: dujella
submitted at: 2026-09-25 19:47:03 UTC
last updated: 2026-09-25 19:47:03 UTC

(-28465592926448050, -9986658729964666636804638)
(28249320354054050, 542210705414253924282462)
(-15291469173181975, -9248260821777444455292138)
(36017445535938650, 2146447264917226301003487)
(33946963722917750, 1516241635846977320628762)
(11870345050407425, 4616510943415456790163462)
(13537794354454250, 4225656968223993402287862)
(-23701351493317975, -9864069141152846242092138)
(30543013939705940, 614058994056949780912212)
(-9337716026000044, -8547807428694198848172201)
(8677307945457380, 5334710580871357201569732)
(10929571604341625, 4832308665083601374170512)
(18782079081299525, 2930616063900065076042612)

found by Elkies (2019)

last edited by dujella at 2026-09-25 19:47:03 UTC · history