Atkin-Lehner |
2- 3- 5+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
121680eg |
Isogeny class |
Conductor |
121680 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
2396160 |
Modular degree for the optimal curve |
Δ |
695761203862530000 = 24 · 38 · 54 · 139 |
Discriminant |
Eigenvalues |
2- 3- 5+ 0 2 13- -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-4139148,-3241016597] |
[a1,a2,a3,a4,a6] |
Generators |
[-1171:450:1] [-309908416:55497879:262144] |
Generators of the group modulo torsion |
j |
63404326912/5625 |
j-invariant |
L |
11.919536326835 |
L(r)(E,1)/r! |
Ω |
0.10584592136507 |
Real period |
R |
28.153036443839 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.000000000029 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
30420o1 40560cy1 121680fo1 |
Quadratic twists by: -4 -3 13 |