curve #1754

y² + xy = x³ − 17113899834684449084840x + 861725639476624934555191308033600

a-invariants: [1, 0, 0, -17113899834684449084840, 861725639476624934555191308033600]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 6234258233715330
discriminant (Δ): 3807449566216760766963721600372291698303621136460371143744000000
Faltings height: 11.3806
naive height: 165.1961
primes of bad reduction: 2, 3, 5, 7, 13, 17, 19, 23, 37, 79, 103, 1021
regulator: 42702989.23629246011509798054432891994951030858
submitted by: hdeping
submitted at: 2026-09-25 11:16:10 UTC
last updated: 2026-09-25 11:16:10 UTC

(124950372231000360766581592316878129104997194119592409842924/1664105024687154868196961314049625705444148508025, -425893619593014532274184730616067434641901400624092035777680791688327216414375211069092/2146698722776984050280502646613694002819608843470820341572203471332610125)
(64136632799879807602358612841404938590464620/1967487766800671287048991958700609, -1605598286087251599753111006585770574701645625577465969275094733780/87270619950531790898523832816705380684409181978977)
(-10927172088347868038383328227397723032064421943114154924180/72731705915593433521848689403017273102934533449, 126695129338187116160762269475173898662103661792253699020686766578648105062870011185980/19614880248323415184607653714174755805645947683742386621613361975412293)
(-335555339776333160442356346369327739333547684368001596750451121425780/30710611197079441922609410479490395447040084273068203534329, 174177450774294034553516102752041834575156826880036703133189347233115391677129218799580335793194393511880/5381863637517311949036196751684776781484841357659780867532080612569778629469324291966733)

Specialization v=-383/553 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 08:31:33 UTC · history