Atkin-Lehner |
2+ 3- 13+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
19344f |
Isogeny class |
Conductor |
19344 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
117504 |
Modular degree for the optimal curve |
Δ |
24626401488 = 24 · 36 · 133 · 312 |
Discriminant |
Eigenvalues |
2+ 3- 0 4 2 13+ -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-703763,227007132] |
[a1,a2,a3,a4,a6] |
Generators |
[3578:11067:8] |
Generators of the group modulo torsion |
j |
2409259817702320384000/1539150093 |
j-invariant |
L |
7.2188033577467 |
L(r)(E,1)/r! |
Ω |
0.73662485792845 |
Real period |
R |
3.2666122518354 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
9672g1 77376bf1 58032g1 |
Quadratic twists by: -4 8 -3 |