curve #1194

y² + xy = x³ − 15075739125931590120183633247999865x + 719481272914731335170056334451666685290651887623417

a-invariants: [1, 0, 0, -15075739125931590120183633247999865, 719481272914731335170056334451666685290651887623417]
rank (lower bound): ≥ 12
torsion subgroup: ℤ/3ℤ
conductor (N): 3663581056152708174921043510992920842747216249770
discriminant (Δ): -4337747574240531256377693575410358534756609615677362919736076334108595909096360787693930381029376000000
Faltings height: 18.5079
naive height: 247.7284
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 43, 47, 59, 61, 71, 11731, 81492408711901957773823
regulator: 20087546112.114865614203990893243765396890241096626249008161134
submitted by: dujella
submitted at: 2026-09-23 21:57:30 UTC
last updated: 2026-09-23 21:57:30 UTC

(89804331152227354, 9479988398821069756793203)
(-62701899104078726, -37659586597332022817662637)
(-13211903879226806, -30271344415900117440882077)
(-10977722414604866, -29726345592837952853574677)
(86749319841487474, 8031086365180078649558563)
(76996051410701074, 3895081239712605109656163)
(76763044815074074, 3814822332867371404251763)
(76160708262893074, 3615100101120986165178763)
(90468440519765674, 9800261165197851637034563)
(6275050034321434, 25002546738193716541475443)
(12762046847775514, 23003533123328924393108083)
(-17295822293641526, -31225864445576588088555437)

found by Eroshkin (2006)

last edited by dujella at 2026-09-23 21:57:30 UTC · history