Atkin-Lehner |
2+ 3- 7+ 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
72072l |
Isogeny class |
Conductor |
72072 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
42240 |
Modular degree for the optimal curve |
Δ |
-16999766784 = -1 · 28 · 36 · 72 · 11 · 132 |
Discriminant |
Eigenvalues |
2+ 3- 3 7+ 11- 13+ 0 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,204,-6172] |
[a1,a2,a3,a4,a6] |
Generators |
[32:-182:1] |
Generators of the group modulo torsion |
j |
5030912/91091 |
j-invariant |
L |
8.2674971060611 |
L(r)(E,1)/r! |
Ω |
0.60062907958028 |
Real period |
R |
0.86029562450176 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000336 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8008b1 |
Quadratic twists by: -3 |