Atkin-Lehner |
3- 5+ 31+ 59+ |
Signs for the Atkin-Lehner involutions |
Class |
82305a |
Isogeny class |
Conductor |
82305 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
2688000 |
Modular degree for the optimal curve |
Δ |
1853411144552803125 = 321 · 55 · 312 · 59 |
Discriminant |
Eigenvalues |
0 3- 5+ -2 3 5 -7 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-8457258,9466339738] |
[a1,a2,a3,a4,a6] |
j |
91766659423791546597376/2542402118728125 |
j-invariant |
L |
0.98076035271209 |
L(r)(E,1)/r! |
Ω |
0.24519010220323 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
27435b1 |
Quadratic twists by: -3 |