Atkin-Lehner |
2+ 3- 11- 17- |
Signs for the Atkin-Lehner involutions |
Class |
12342p |
Isogeny class |
Conductor |
12342 |
Conductor |
∏ cp |
27 |
Product of Tamagawa factors cp |
deg |
45936 |
Modular degree for the optimal curve |
Δ |
-56869839847062 = -1 · 2 · 33 · 118 · 173 |
Discriminant |
Eigenvalues |
2+ 3- 0 -4 11- -4 17- -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-20936,-1222828] |
[a1,a2,a3,a4,a6] |
j |
-4734057625/265302 |
j-invariant |
L |
0.59341534656101 |
L(r)(E,1)/r! |
Ω |
0.19780511552034 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
98736cj1 37026bb1 12342bb1 |
Quadratic twists by: -4 -3 -11 |