Atkin-Lehner |
3- 11- 31- |
Signs for the Atkin-Lehner involutions |
Class |
31713h |
Isogeny class |
Conductor |
31713 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
111104 |
Modular degree for the optimal curve |
Δ |
-872507531302143 = -1 · 3 · 11 · 319 |
Discriminant |
Eigenvalues |
-1 3- -2 -2 11- -2 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,10551,-1357680] |
[a1,a2,a3,a4,a6] |
j |
4913/33 |
j-invariant |
L |
0.4981694029799 |
L(r)(E,1)/r! |
Ω |
0.24908470149582 |
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 |
95139e1 31713b1 |
Quadratic twists by: -3 -31 |