Atkin-Lehner |
2+ 13- 37- |
Signs for the Atkin-Lehner involutions |
Class |
30784i |
Isogeny class |
Conductor |
30784 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
58368 |
Modular degree for the optimal curve |
Δ |
21309423616 = 218 · 133 · 37 |
Discriminant |
Eigenvalues |
2+ 0 2 2 2 13- -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-108364,13730160] |
[a1,a2,a3,a4,a6] |
Generators |
[165:585:1] |
Generators of the group modulo torsion |
j |
536832589893417/81289 |
j-invariant |
L |
6.8243284680351 |
L(r)(E,1)/r! |
Ω |
0.94692825646184 |
Real period |
R |
2.4022687468546 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999998 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
30784p1 481a1 |
Quadratic twists by: -4 8 |