curve #313

y² + xy + y = x³ − x² − 220168815383488457944879718815779326933313515572495053707x + 1257194842755882887406594337014748119778734089385499851686385036711122100696018139931

a-invariants: [1, -1, 1, -220168815383488457944879718815779326933313515572495053707, 1257194842755882887406594337014748119778734089385499851686385036711122100696018139931]
rank (lower bound): ≥ 15
torsion subgroup: ℤ/2ℤ
conductor (N): 14143803817470093613466453371895612334117548667434143819728526037275098905399795800409355189270
naive height: 400.8156
Faltings height: 31.1161
discriminant (Δ): 249178700214336462700040090529345761697029666451736506636521278574102532187649713021760375104270067437065715167209867291412637269415937398182192231222662235033600000000
primes of bad reduction: 2, 3, 5, 7, 13, 17, 19, 23, 31, 79, 131, 137, 227, 229, 337, 443, 593, 751, 1093, 1297, 2113, 8231, 8629, 19937, 33073, 47419, 157559, 479081, 858259, 2391953, 11332579
regulator: 221168458383089576023399.93447943382901055717981730453454288681861498
submitted by: 7fff-zip
submitted at: 2026-08-24 00:24:06 UTC
last updated: 2026-08-24 00:24:06 UTC

Witness: 15 independent points

(12952802258768037562920419691, 760624237746275145822530527782809048420554)
(9296759061407832022961892091, -117706329405909581096723749234216789621046)
(222624245683601369567481529011/25, -6553654165046182125480094737906217281011806/125)
(8745147724266533162314154991, -24372398301247644390390545705912060927846)
(9348862375787350187490292075, -126368262383604274172514200984160169234998)
(22128094639988878567097078575, 2687072183971838200591523573881539275509302)
(123256580993056065887959322991, 42972743576774831549985350723511924134323354)
(9152540081885463056412080491, -93754857572604587970642189102079746273846)
(23934693908111273740405892091, 3114318465555463902173558963510640786928954)
(232479815103417622852482482094744751/26204161, -6279157699772032905579917676995179678549875266153114/134139100159)
(47469880134902568236841334183887331/2627641, 7590471901306372528055259960134774243722887164840194/4259406061)
(6303291725423904694529517774006850875/632975281, 3639199527244617145007807690315649601734819873776118118/15925025094679)
(18649366282820888528918554221888807958879/2131199978769, -79058889948001018678575321163989827935675817610140699310662/3111259994605648647)
(3302124924467545201908104886196734257499/381203751889, 591828536888659339121378411565207336357351852617288681402/235361676880050713)
(15192142299356308321276671412389075622291/22590390601, 1872076927678462555210496242273744693779322661236943964552354/3395358297720901)

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