curve #1866

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y² = x³ + x² − 79153117356568074900688747866481878240x + 262103581218105769722387293850076510690437243123149589588

a-invariants

[0, 1, 0, -79153117356568074900688747866481878240, 262103581218105769722387293850076510690437243123149589588]

rank (lower bound)

≥ 24

torsion subgroup

trivial

conductor (N)

19763022894623766612923307837566921631556312466038828830623669818407645633469665742433520

discriminant (Δ)

2060667975321087068778846717703684481203522819128318699043060992311538103389743123366879556283259144676960480000000

Faltings height

20.7034

naive height

273.4069

primes of bad reduction

2, 3, 5, 7, 11, 13, 19, 23, 37, 443, 1961194791395055751, 2976806284656805802648659711, 178836918111644329249463610289

regulator

2184355324581442073615618.1853624804009584086512031922740436840870035616454117713783016

submitted by

Ritik Jain

submitted at

2026-09-25 17:20:56 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 17:24:46 UTC

Witness: 24 independent points log in to add more points →

(1352010071156871823650911924964/332182780609, 519657755655335141572900090261451946724436550/191454542152338977)
(-2271463460362745004, 20740715375425769261987398950)
(9927343744562789046, -21323331928448814285544079700)
(4338837468509366646, 593212055141945790596164500)
(2602002950982900396, 8588573072573061708542288250)
(62618117797960310658824948600119252294854/19308056210942599285249, -16864382495934960711737172510697166826502665156308127297133500/2682920672032935276974173862514943)
(969010175749309152246, 30162981204179247150398211239700)
(58603869150723371961/16, -295540826492716848877025251125/64)
(502230886713277900326, -11253495029737011617378208930660)
(36158468716344680766, 211364354951882589448143193860)
(36133570058994648909/4, -134872248486622882240039814325/8)
(13426351566064463286, -40245409614358477306498269780)
(141426972616963495097049/35344, 20422189596079430734197247037276325/6644672)
(-9092734890797275729191/1024, -533238554978687427292976336378595/32768)
(-1408857789573926604, -19256756038945224679440555750)
(-22609403742571180686666/2209, -19500202559654041169888440504020/103823)
(1855551482772490976006/961, -321506890974083868060544775492100/29791)
(5094555327546385489655344752566251494/2381127868383471769, 37207630947661415572907841668544741049197428197966433820/3674295466773267675226462147)
(-944046662615186409199267319086687791/103094377654929424, 489940200960162252491021304103373473234335601407292095/33101865669035554696875968)
(962292961363177107562046130094179/159255238011769, 4235821316644550438008675423299117533393480213580/2009743294057126507853)
(18111634926522294490385602777/56021209344, 203933055892052532738552736606409002287903389/13259547997212672)
(-97766484926845818, 16426842934449606241059318660)
(-360718543216255242186964/39601, 118819496282334236084258449126679670/7880599)
(-7086121863987866604, 21614252415170892947583164250)

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