Atkin-Lehner |
2+ 3- 5+ 13- 37+ |
Signs for the Atkin-Lehner involutions |
Class |
57720i |
Isogeny class |
Conductor |
57720 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
516096 |
Modular degree for the optimal curve |
Δ |
725652281972966400 = 210 · 316 · 52 · 13 · 373 |
Discriminant |
Eigenvalues |
2+ 3- 5+ 2 -2 13- 0 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-306976,-51149776] |
[a1,a2,a3,a4,a6] |
Generators |
[-193:972:1] |
Generators of the group modulo torsion |
j |
3124197198379700356/708644806614225 |
j-invariant |
L |
7.6909974439047 |
L(r)(E,1)/r! |
Ω |
0.20612539412942 |
Real period |
R |
2.3320141716003 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000157 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
115440c1 |
Quadratic twists by: -4 |