Atkin-Lehner |
2+ 5- 7- 11+ |
Signs for the Atkin-Lehner involutions |
Class |
12320d |
Isogeny class |
Conductor |
12320 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
-19841483200 = -1 · 26 · 52 · 7 · 116 |
Discriminant |
Eigenvalues |
2+ 2 5- 7- 11+ -4 -8 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-210,-6808] |
[a1,a2,a3,a4,a6] |
Generators |
[7134:31445:216] |
Generators of the group modulo torsion |
j |
-16079333824/310023175 |
j-invariant |
L |
6.9384375723688 |
L(r)(E,1)/r! |
Ω |
0.52463357694482 |
Real period |
R |
6.612651074274 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
12320i1 24640q2 110880dh1 61600be1 |
Quadratic twists by: -4 8 -3 5 |