Atkin-Lehner |
2+ 5+ 13+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
32240a |
Isogeny class |
Conductor |
32240 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
-1133300480 = -1 · 28 · 5 · 134 · 31 |
Discriminant |
Eigenvalues |
2+ -1 5+ -4 0 13+ -3 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,239,701] |
[a1,a2,a3,a4,a6] |
Generators |
[28:169:1] |
Generators of the group modulo torsion |
j |
5872987136/4426955 |
j-invariant |
L |
2.1069432979721 |
L(r)(E,1)/r! |
Ω |
0.98835181271879 |
Real period |
R |
1.0658873039229 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999992 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
16120d1 128960bj1 |
Quadratic twists by: -4 8 |