Atkin-Lehner |
2+ 3- 7- 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
72072r |
Isogeny class |
Conductor |
72072 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
57344 |
Modular degree for the optimal curve |
Δ |
-576684396288 = -1 · 28 · 38 · 74 · 11 · 13 |
Discriminant |
Eigenvalues |
2+ 3- 0 7- 11- 13- 0 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1335,-41078] |
[a1,a2,a3,a4,a6] |
Generators |
[83:648:1] |
Generators of the group modulo torsion |
j |
-1409938000/3090087 |
j-invariant |
L |
6.9354412409075 |
L(r)(E,1)/r! |
Ω |
0.36977072273173 |
Real period |
R |
2.3445072898529 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001093 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
24024bb1 |
Quadratic twists by: -3 |