Atkin-Lehner |
2+ 17+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
4216a |
Isogeny class |
Conductor |
4216 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
144 |
Modular degree for the optimal curve |
Δ |
-8432 = -1 · 24 · 17 · 31 |
Discriminant |
Eigenvalues |
2+ -1 0 2 3 0 17+ -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-8,13] |
[a1,a2,a3,a4,a6] |
Generators |
[2:1:1] |
Generators of the group modulo torsion |
j |
-4000000/527 |
j-invariant |
L |
3.2469555430359 |
L(r)(E,1)/r! |
Ω |
4.0068106530713 |
Real period |
R |
0.40517955852831 |
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 |
8432c1 33728a1 37944l1 105400o1 |
Quadratic twists by: -4 8 -3 5 |