Atkin-Lehner |
2+ 13+ 83+ |
Signs for the Atkin-Lehner involutions |
Class |
69056b |
Isogeny class |
Conductor |
69056 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
4073472 |
Modular degree for the optimal curve |
Δ |
-9.1272883738522E+21 |
Discriminant |
Eigenvalues |
2+ -1 -3 -1 6 13+ -3 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,4920863,-1865755039] |
[a1,a2,a3,a4,a6] |
Generators |
[354032155:22249375744:205379] |
Generators of the group modulo torsion |
j |
50269842484372470023/34817842002305024 |
j-invariant |
L |
3.1081136880642 |
L(r)(E,1)/r! |
Ω |
0.073432589829361 |
Real period |
R |
5.2907600257386 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000003922 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69056m1 2158b1 |
Quadratic twists by: -4 8 |