curve #4084

y² + xy = x³ − 1045076954961291136981343863584158030259957920237050x + 7564150446757322267827171161572298959878730920434682147066629995892185622500

a-invariants: [1, 0, 0, -1045076954961291136981343863584158030259957920237050, 7564150446757322267827171161572298959878730920434682147066629995892185622500]
c-invariants: [50163693838141974575104505452039585452477980171378401, -6535425985998326439402675958844007058548185377912323553124946495167818634907601]
rank (lower bound): ≥ 20
torsion subgroup: ℤ/2ℤ
conductor (N): 735726883900703598396459076522528622439471321942270014656714425868103908609679211118354170
discriminant (Δ): 48333295546751134599638512816732544086013922472230126085692862943390177763000691660861637779570038549767110674953262550022795140490805944466104830894080000
Faltings height: 28.3803
naive height: 364.0414
primes of bad reduction: 2, 3, 5, 7, 11, 13, 31, 43, 79, 109, 113, 127, 149, 157, 293, 487, 499, 863, 1319, 1481, 1489, 4561, 4943, 7079, 11549, 28433, 40879, 108643, 1185883, 2048521, 5719267
regulator: 167757052801705547031091.357799176387758111805133955885504316938189366237747359
submitted by: wgxli
submitted at: 2026-10-09 05:51:40 UTC
last updated: 2026-10-09 05:51:40 UTC

(612481462763842797414200, 83212318481234937009598135603932156050)
(7595954208428351231772332, 8004315770756941150043534716779660566)
(1626002709202146418185460, 76610387353999380249902549594379307990)
(3263949970943965655060312, 64713550472543558317668001064535577586)
(4182962743731625953475070, 57147375448505840623893709394572688330)
(5900630179507838401198910, 40037265679360838843281267846157529290)
(5975277638349797406071060, 39151838510685004223873168051156750390)
(7371921565790759992671956, 16141680820293020767326958373679042422)
(28292752046375188637375252, 25373693258509255132539955751180465846)
(30260614855486303009166510, 60409186705246172403594394323386055050)
(-33599229896391872440583518, 68901984765705989622514226950995134666)
(-9928034086241999194822444, 130234960177456035706651879357734816182)
(33910293302904330978206060, 105446676838200510747292003327841878550)
(34020066264574542813227450, 106696738805937382649581951700633318300)
(55504534464152405805391220, 347208036853374825876629959331579991350)
(70104829201770377080088780, 528055401599478472608584685658427699870)
(-27827861946128397170995948, 122869005160433283881857529657614309046)
(114459691138695909330430990, 1177915009783656398018720019350335177960)
(132858874002752047322971556, 1487908671108469144309045552007020747382)
(134346982126064600605484200, 1513936884362038707017488874752729137250)

2-isogenous to curve #4083

last edited by wgxli at 2026-10-09 05:51:41 UTC · history