Atkin-Lehner |
2+ 5- 19- 43- |
Signs for the Atkin-Lehner involutions |
Class |
8170c |
Isogeny class |
Conductor |
8170 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
7680 |
Modular degree for the optimal curve |
Δ |
-7550387200 = -1 · 210 · 52 · 193 · 43 |
Discriminant |
Eigenvalues |
2+ 0 5- -3 -6 0 -7 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-509,6213] |
[a1,a2,a3,a4,a6] |
Generators |
[-22:91:1] [20104:-119397:512] |
Generators of the group modulo torsion |
j |
-14600136398121/7550387200 |
j-invariant |
L |
4.0816615235103 |
L(r)(E,1)/r! |
Ω |
1.2281723474735 |
Real period |
R |
0.27694684788525 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999969 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
65360g1 73530bf1 40850h1 |
Quadratic twists by: -4 -3 5 |