Atkin-Lehner |
2- 5+ 7+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
17360p |
Isogeny class |
Conductor |
17360 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
-30486937600 = -1 · 214 · 52 · 74 · 31 |
Discriminant |
Eigenvalues |
2- 0 5+ 7+ -2 -2 0 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-2603,51802] |
[a1,a2,a3,a4,a6] |
Generators |
[-27:320:1] [21:80:1] |
Generators of the group modulo torsion |
j |
-476196576129/7443100 |
j-invariant |
L |
6.4157135883869 |
L(r)(E,1)/r! |
Ω |
1.1773399364295 |
Real period |
R |
1.3623324474672 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999994 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
2170m1 69440dc1 86800bo1 121520cw1 |
Quadratic twists by: -4 8 5 -7 |