curve #1861

y² + xy = x³ − 1209873315556653510389989204544209972082084x + 331058311839965956052748107957148273288865814054655695750098704

a-invariants: [1, 0, 0, -1209873315556653510389989204544209972082084, 331058311839965956052748107957148273288865814054655695750098704]
rank (lower bound): ≥ 12
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 31023331291622976051227194580729790167205619926
discriminant (Δ): 65997266097051072688611154713359254284275525658487439540418783678270245939901028339360764864238478689831866483966067020194709504
Faltings height: 23.2286
naive height: 302.3109
primes of bad reduction: 2, 3, 7, 13, 29, 31, 43, 73, 79, 83, 89, 151, 199, 239, 263, 601, 617, 1433, 3449, 6199, 1607849
regulator: 312848498549.62405624139280925577340874383690316899070741394065
submitted by: dujella
submitted at: 2026-09-25 17:15:28 UTC
last updated: 2026-09-25 17:15:28 UTC

(-29781155673654532760, -19158896731680436660803850599908)
(983416510666458000520, 9608273788334829529339520513308)
(224964958024936465672, 8382393215379522545608441887004)
(-477578685523836137672, -28283231850374324028595134427604)
(7181676589197025172320, 601704020748289548363284118568708)
(5837278004406510341704, 438368588436251112531715221250204)
(-19227536967843022106, -18823232648923373557639136562398)
(-76496145458495433471695/64, -4271175174781071803481436995763861/512)
(-73289325270983337128, -20477681753542264917803095171316)
(-128930895710341262696, -22020561326941424170553666911796)
(7048140466716542287624/25, 439674172988024494810579430888108/125)
(23072175510651402246256/25, 90457445883648067024579307809964/125)

found by Eroshkin (2008)

last edited by dujella at 2026-09-25 17:15:29 UTC · history