Atkin-Lehner |
2- 7- 13+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
68432n |
Isogeny class |
Conductor |
68432 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
-14233856 = -1 · 28 · 7 · 132 · 47 |
Discriminant |
Eigenvalues |
2- -1 -3 7- -3 13+ -2 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-92,-356] |
[a1,a2,a3,a4,a6] |
Generators |
[17:52:1] |
Generators of the group modulo torsion |
j |
-340062928/55601 |
j-invariant |
L |
2.7857574074327 |
L(r)(E,1)/r! |
Ω |
0.76322455961935 |
Real period |
R |
1.8249919844037 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000797 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
17108b1 |
Quadratic twists by: -4 |