Atkin-Lehner |
2+ 3- 7+ 43- |
Signs for the Atkin-Lehner involutions |
Class |
86688k |
Isogeny class |
Conductor |
86688 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
30720 |
Modular degree for the optimal curve |
Δ |
-603868608 = -1 · 26 · 36 · 7 · 432 |
Discriminant |
Eigenvalues |
2+ 3- 0 7+ 0 -6 -6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-45,-1188] |
[a1,a2,a3,a4,a6] |
Generators |
[184:2494:1] |
Generators of the group modulo torsion |
j |
-216000/12943 |
j-invariant |
L |
4.8277327880085 |
L(r)(E,1)/r! |
Ω |
0.71601994624605 |
Real period |
R |
3.3712278605787 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000010313 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
86688br1 9632e1 |
Quadratic twists by: -4 -3 |