Atkin-Lehner |
3+ 5- 7+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
47775ba |
Isogeny class |
Conductor |
47775 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
483840 |
Modular degree for the optimal curve |
Δ |
-192947439094921875 = -1 · 3 · 58 · 78 · 134 |
Discriminant |
Eigenvalues |
0 3+ 5- 7+ 2 13- 6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,142917,3717818] |
[a1,a2,a3,a4,a6] |
Generators |
[376:10510:1] |
Generators of the group modulo torsion |
j |
143360000/85683 |
j-invariant |
L |
4.5442926763544 |
L(r)(E,1)/r! |
Ω |
0.19479161138002 |
Real period |
R |
1.944082980161 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000022 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
47775bv1 47775df1 |
Quadratic twists by: 5 -7 |