Atkin-Lehner |
2+ 3- 7- 11+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
85008t |
Isogeny class |
Conductor |
85008 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
131072 |
Modular degree for the optimal curve |
Δ |
-1656565432368 = -1 · 24 · 3 · 7 · 118 · 23 |
Discriminant |
Eigenvalues |
2+ 3- -2 7- 11+ -2 -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-4719,-140880] |
[a1,a2,a3,a4,a6] |
Generators |
[12880:86376:125] [432240:3952936:3375] |
Generators of the group modulo torsion |
j |
-726516846671872/103535339523 |
j-invariant |
L |
11.923209773895 |
L(r)(E,1)/r! |
Ω |
0.28574702415375 |
Real period |
R |
83.452906005114 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999352 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
42504n1 |
Quadratic twists by: -4 |