Atkin-Lehner |
2+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
1216b |
Isogeny class |
Conductor |
1216 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
384 |
Modular degree for the optimal curve |
Δ |
-39845888 = -1 · 221 · 19 |
Discriminant |
Eigenvalues |
2+ -1 0 -1 6 -5 3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-993,12385] |
[a1,a2,a3,a4,a6] |
Generators |
[9:64:1] |
Generators of the group modulo torsion |
j |
-413493625/152 |
j-invariant |
L |
2.2319890458138 |
L(r)(E,1)/r! |
Ω |
2.0053183057831 |
Real period |
R |
0.27825869830454 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
1216o1 38a3 10944l1 30400d1 |
Quadratic twists by: -4 8 -3 5 |