Atkin-Lehner |
2- 3- 11- 43+ |
Signs for the Atkin-Lehner involutions |
Class |
68112ca |
Isogeny class |
Conductor |
68112 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
64512 |
Modular degree for the optimal curve |
Δ |
-2050761867264 = -1 · 214 · 37 · 113 · 43 |
Discriminant |
Eigenvalues |
2- 3- -1 1 11- -4 -3 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-3963,118186] |
[a1,a2,a3,a4,a6] |
Generators |
[-67:288:1] [45:176:1] |
Generators of the group modulo torsion |
j |
-2305199161/686796 |
j-invariant |
L |
10.153446830552 |
L(r)(E,1)/r! |
Ω |
0.7835365250642 |
Real period |
R |
0.26996845142069 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000002 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8514i1 22704be1 |
Quadratic twists by: -4 -3 |