Atkin-Lehner |
3- 13+ 103- |
Signs for the Atkin-Lehner involutions |
Class |
52221h |
Isogeny class |
Conductor |
52221 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
169344 |
Modular degree for the optimal curve |
Δ |
-337509401544471 = -1 · 3 · 139 · 1032 |
Discriminant |
Eigenvalues |
1 3- -2 2 -4 13+ -6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,17403,-17405] |
[a1,a2,a3,a4,a6] |
Generators |
[438400797315:-17289407344097:291434247] |
Generators of the group modulo torsion |
j |
120773549807/69923919 |
j-invariant |
L |
6.5515530429434 |
L(r)(E,1)/r! |
Ω |
0.32192936277009 |
Real period |
R |
20.350902404543 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000008 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
4017c1 |
Quadratic twists by: 13 |