Atkin-Lehner |
13+ 61+ |
Signs for the Atkin-Lehner involutions |
Class |
10309a |
Isogeny class |
Conductor |
10309 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
4680 |
Modular degree for the optimal curve |
Δ |
-294435349 = -1 · 136 · 61 |
Discriminant |
Eigenvalues |
1 -2 3 -1 5 13+ 4 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-342,2537] |
[a1,a2,a3,a4,a6] |
Generators |
[5:28:1] |
Generators of the group modulo torsion |
j |
-912673/61 |
j-invariant |
L |
4.5900638610874 |
L(r)(E,1)/r! |
Ω |
1.7010417214508 |
Real period |
R |
2.698384056784 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
92781j1 61a1 |
Quadratic twists by: -3 13 |