Atkin-Lehner |
3- 5+ 17- 89- |
Signs for the Atkin-Lehner involutions |
Class |
68085i |
Isogeny class |
Conductor |
68085 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
4193280 |
Modular degree for the optimal curve |
Δ |
-1.0733041989569E+22 |
Discriminant |
Eigenvalues |
-2 3- 5+ -1 3 2 17- 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,190797,-4984373142] |
[a1,a2,a3,a4,a6] |
j |
1053685028089032704/14722965692138671875 |
j-invariant |
L |
0.94649083543967 |
L(r)(E,1)/r! |
Ω |
0.059155676587837 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
22695i1 |
Quadratic twists by: -3 |