Atkin-Lehner |
2+ 3- 7+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
38304o |
Isogeny class |
Conductor |
38304 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
540672 |
Modular degree for the optimal curve |
Δ |
158333584115294784 = 26 · 318 · 72 · 194 |
Discriminant |
Eigenvalues |
2+ 3- -2 7+ 0 -6 -2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1579161,763574240] |
[a1,a2,a3,a4,a6] |
Generators |
[373:15048:1] |
Generators of the group modulo torsion |
j |
9334594126684326592/3393638205489 |
j-invariant |
L |
3.6460649567618 |
L(r)(E,1)/r! |
Ω |
0.31781745339587 |
Real period |
R |
2.868049660114 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
38304s1 76608dw2 12768m1 |
Quadratic twists by: -4 8 -3 |