curve #1753

y² + xy = x³ − 119171449305893243756x + 492853003940065316232614981520

a-invariants: [1, 0, 0, -119171449305893243756, 492853003940065316232614981520]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 1549970045933610
discriminant (Δ): 3382439438496234148210531605742464914956148408756289118310400
Faltings height: 10.4098
naive height: 150.2949
primes of bad reduction: 2, 3, 5, 7, 17, 37, 109, 293, 461, 797
regulator: 57337916.09393910883718147528057120709205899089
submitted by: hdeping
submitted at: 2026-09-25 11:15:44 UTC
last updated: 2026-09-25 11:15:44 UTC

(30461613843210531316724882822372298688357656541601082349944/10429123227214771998057697516290583465359451840249, 13873994256475308465103656991606592561770694555776543643839087048164107059556209177919292/33679970191994122715261549519207215467008391528341291884338637214778467443)
(163285934557019657360022451900937500239253669763800711015471826686/29587662787539522691698961472802942757659380248348647121, 9187085052557392303704226350388092099909055989370076688882915321848704907031162722843139753171920/160940738776354943846519173807564808434821205761666942226123906711289420564054333081)
(12245292449950858866732737197559930448829840792350136/2229264778562522519411354461511920268232241, -210138417778625923473073385220343419190953751306875614434561541880613557323764/3328453404785252656999426430031889963021187627509024873451774039)
(19404318726042170362883867668246505186586955475726768938057221342424/112218592391203080042957001776659238552645934632213818209, 85310137886623626735859439885160282230512277950509762664684849295616753860268017576964052857266456492/1188768326578197360476373874981898418651017755969002712974526672215306206081642131823)

Specialization v=377/545 of the Dujella-Peral torsion Z/2xZ/6 family y^2=x^3+A26(v)x^2+B26(v)x (Contemp. Math. 649, sec 2.2).

last edited by hdeping at 2026-09-27 08:31:18 UTC · history