curve #1974

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y² + xy = x³ − 2059175582472059996102269978595x + 1091552419888384223929967894357502320397905025

a-invariants

[1, 0, 0, -2059175582472059996102269978595, 1091552419888384223929967894357502320397905025]

rank (lower bound)

≥ 21

torsion subgroup

trivial

conductor (N)

124492640486680357357487598711564568239868262373037616568401683463377230

discriminant (Δ)

44082533049077472475466474960705349762688995961679474477243468556132852584149421391360000000

Faltings height

16.3467

naive height

221.0132

primes of bad reduction

2, 3, 5, 13, 19, 41, 173, 463, 7043396929579, 726327279713681044054805798950074428980593270823

regulator

84218684746764456333.789536074564595176308267301643737822705051403596118606651915

submitted by

Ritik Jain

submitted at

2026-09-25 20:07:26 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 20:09:43 UTC

Witness: 21 independent points log in to add more points →

(24877660078884090, -3917473359929274784884795)
(100607738732105433149773837242218555086/146066317875685751357025, -2636439162349042190353993031711412182142026230650702151/55824536022761360720850508683428625)
(3169827523857262, 162524257153527803511337)
(-38831573699289290/49, 16181863279970991225326215/343)
(9564980407045240, -925464557222049266307695)
(994037672205742, 5183991202768670492521)
(-974367894897374, -46614258476078090198483)
(674980288591930, 3028105295709776566465)
(467958475155581290/961, -425816753932957483091858645/29791)
(33622162336307638/49, 444452011643118462958591/343)
(686168056659630, -1295410180502086895895)
(391719298610830, 18575267892376744684105)
(-527490360599498, 45066346522039944040561)
(1068221364646990, 10528111340004440699305)
(17130079963642846/25, -189735540572716038379771/125)
(3156814109661785230/2601, -2586441155804002641951259085/132651)
(106688208379186814372710/69939769, -22653340885169927485696642267667365/584906288147)
(104299132631213902571844424419337661929390/159529490287934115619589089, 10021999856397916570796560351443475152618968672224821651685945/2014936974711362685000950904240007641937)
(-1478560153277542827440413502659285061279586500160650/1447517503757703397614127670825806041, 80360031204070683099652890293184164833013759654355004548456658816580555563445/1741549151697604761456395464126686034544050814390210589)
(41006160380694381635985510460073700120569740/165521647750350094946606254561, 1644867210633499614417633309443295808836270391971416393171435989655/67341409396927419224324506310823625715382191)
(22870815699258152012139412313344899932406190/96656764315885171433714077441, 746772198819189794836427888399147571292473354667789408195115398505/30050270029260699576319328303058789474309761)

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