Atkin-Lehner |
2+ 5- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
12200c |
Isogeny class |
Conductor |
12200 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
10240 |
Modular degree for the optimal curve |
Δ |
30500000000 = 28 · 59 · 61 |
Discriminant |
Eigenvalues |
2+ 0 5- 0 6 4 -2 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-2375,-43750] |
[a1,a2,a3,a4,a6] |
j |
2963088/61 |
j-invariant |
L |
2.7389696053379 |
L(r)(E,1)/r! |
Ω |
0.68474240133448 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
24400g1 97600bf1 109800cb1 12200k1 |
Quadratic twists by: -4 8 -3 5 |