Atkin-Lehner |
2+ 3+ 13+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
47424c |
Isogeny class |
Conductor |
47424 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
96768 |
Modular degree for the optimal curve |
Δ |
-80782597029888 = -1 · 225 · 33 · 13 · 193 |
Discriminant |
Eigenvalues |
2+ 3+ 0 -1 -3 13+ 6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-9953,580449] |
[a1,a2,a3,a4,a6] |
Generators |
[-119:256:1] |
Generators of the group modulo torsion |
j |
-415996269625/308161152 |
j-invariant |
L |
4.3071391203463 |
L(r)(E,1)/r! |
Ω |
0.56015503487064 |
Real period |
R |
1.9222977801725 |
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 |
47424dc1 1482e1 |
Quadratic twists by: -4 8 |