curve #1199

y² + xy = x³ − 91850566882818096919315x + 1037306571339910255836508005644277281

a-invariants: [1, 0, 0, -91850566882818096919315, 1037306571339910255836508005644277281]
rank (lower bound): ≥ 14
torsion subgroup: ℤ/2ℤ
conductor (N): 40191415156983276757320394144365170036138946
discriminant (Δ): -464784533127967164556282917220292808999166989979714346135718665034210252288
Faltings height: 13.0062
naive height: 179.3825
primes of bad reduction: 2, 3, 7, 11, 19, 41, 53, 71, 101, 199, 239, 347, 353, 431, 2341, 3923, 5813, 31957
regulator: 92777427372277.5716493064830980121725105183921635332294948810618489
submitted by: dujella
submitted at: 2026-09-23 22:30:11 UTC
last updated: 2026-09-23 22:30:11 UTC

(-996479609134, -373306111797408307)
(1931413067938, 2839851910855975069)
(2368432972490, 3755718401298815621)
(-22038014750746/25, -82278434916377213243/125)
(-45431381814754/49, -195668853202643488417/343)
(15929753656846/9, 68410268470418517715/27)
(120539589837944, 1323406612061547270311)
(-76374786569194/169, -2182139658362122909315/2197)
(4322187601621/16, 65022456752560397389/64)
(-1042515559102, -3995834311749247)
(-656482032314, -902596833950329079)
(142736460327974/625, 15844097570647185301457/15625)
(-959497727296, -492024863758482385)
(14049252923996084/11449, 2039761707301937603588713/1225043)

found by Dujella (2009)

last edited by dujella at 2026-09-23 22:30:12 UTC · history