curve #1101

y² + xy = x³ − 1243378215801409573671681394724148505836465x + 533568551747456170418786926292796873632980274337049541031491817

a-invariants: [1, 0, 0, -1243378215801409573671681394724148505836465, 533568551747456170418786926292796873632980274337049541031491817]
rank (lower bound): ≥ 17
torsion subgroup: ℤ/2ℤ
conductor (N): 483715857041459117037004194204697257455321027821861096646780904570
discriminant (Δ): 35557137322511646942101692043817738601945628983992174523985844638015717784037297797577744313243324223699408067381500000000000
Faltings height: 22.9067
naive height: 302.3928
primes of bad reduction: 2, 3, 5, 7, 11, 23, 31, 37, 41, 223, 241, 307, 311, 337, 379, 433, 743, 1873, 2801, 3617, 8179, 14879, 407599
regulator: 116452354976420576.061197814451685069772958085566197818207468993161227619
submitted by: dujella
submitted at: 2026-09-23 19:30:00 UTC
last updated: 2026-09-23 19:30:00 UTC

(295909366620588641274, 13840224417503771788066682779563)
(635444448565646044074, 238026802184285253010435263963)
(406841929406614922574, 9749398968236802857137233294963)
(-498536763048246361848, -32086329206297967537307675521387)
(365329877709573516324, 11317439122188943552599543969963)
(653658047088929911074, 334802329486502314680260310963)
(390116221121923660074, 10386461778331482325086438819963)
(4686357172719668406771/4, 209378289880549899790913148373779/8)
(620651162007351845724, 971661597627620215237774115163)
(-174087993049324255086, -27290103511304743453323169025397)
(601743991009112691324, 1806148426566753856090607319963)
(-69410472226008425466, -24890512532673385235973153079977)
(-334709979328169335446, -30203341402018178778521393923557)
(628923493523439835074, 588364888705804863742467594963)
(594390299829369312882, 2124756989643788803088946333003)
(659600354729670357324, 640233767104009049626213294713)
(137924634886574871255456/169, 17355263577043625203177043015047311/2197)

found by Dujella (2009)

last edited by dujella at 2026-09-23 19:30:00 UTC · history