curve #1195

y² + xy = x³ − 19381405000232295858279660x + 32840137866325074034091731864481219472

a-invariants: [1, 0, 0, -19381405000232295858279660, 32840137866325074034091731864481219472]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/3ℤ
conductor (N): 3349215178151004720224491308022110 ☆ record for ℤ/3ℤ torsion, rank ≥ 11
discriminant (Δ): 45117023666726631343819195697345509108383122663276932923252354613248000000 ☆ record for ℤ/3ℤ torsion, rank ≥ 11
Faltings height: 13.1978 ☆ record for ℤ/3ℤ torsion, rank ≥ 11
naive height: 186.2927 ☆ record for ℤ/3ℤ torsion, rank ≥ 11
primes of bad reduction: 2, 3, 5, 11, 13, 19, 23, 37, 43, 67, 103, 2113, 4099, 160981, 8976907
regulator: 96975383.0479199387633077199976953976019107591692857720043361
submitted by: dujella
submitted at: 2026-09-23 22:02:22 UTC
last updated: 2026-09-23 22:02:22 UTC

(2055128982024, 1299537851617235028)
(2558537333184, 23764901654317908)
(2560149274944, 31604788042325868)
(724785670584, 4378756710176644308)
(2153616502584, 1043375878842321108)
(2560641704024, 33755458168724948)
(2582011626312, 104107876468451940)
(384922167384, 5043494376631511508)
(2582080359834, 104312168121256608)
(3706952400984, 3454453825643044308)
(2563692341592, 45752868317464788)

found by Eroshkin (2023)

last edited by dujella at 2026-09-23 22:02:22 UTC · history