Atkin-Lehner |
2- 3+ 13+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
117312bt |
Isogeny class |
Conductor |
117312 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
580608 |
Modular degree for the optimal curve |
Δ |
-473594452770816 = -1 · 221 · 37 · 133 · 47 |
Discriminant |
Eigenvalues |
2- 3+ 1 -3 6 13+ 2 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-28705,2154433] |
[a1,a2,a3,a4,a6] |
Generators |
[189:1856:1] |
Generators of the group modulo torsion |
j |
-9978645018889/1806619464 |
j-invariant |
L |
5.5609919111038 |
L(r)(E,1)/r! |
Ω |
0.50511936000052 |
Real period |
R |
2.7523157030647 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000225316 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117312s1 29328w1 |
Quadratic twists by: -4 8 |