Atkin-Lehner |
7- 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
13013m |
Isogeny class |
Conductor |
13013 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
169344 |
Modular degree for the optimal curve |
Δ |
-53201141892899 = -1 · 72 · 113 · 138 |
Discriminant |
Eigenvalues |
2 -3 3 7- 11+ 13+ -8 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-33631,2399673] |
[a1,a2,a3,a4,a6] |
j |
-871531204608/11022011 |
j-invariant |
L |
2.5314159869206 |
L(r)(E,1)/r! |
Ω |
0.63285399673015 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117117by1 91091g1 1001c1 |
Quadratic twists by: -3 -7 13 |