Atkin-Lehner |
2+ 3- 7- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
68544bz |
Isogeny class |
Conductor |
68544 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
147456 |
Modular degree for the optimal curve |
Δ |
-117890661482496 = -1 · 224 · 310 · 7 · 17 |
Discriminant |
Eigenvalues |
2+ 3- -2 7- -2 -4 17+ 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-12396,-745040] |
[a1,a2,a3,a4,a6] |
Generators |
[4184:270540:1] |
Generators of the group modulo torsion |
j |
-1102302937/616896 |
j-invariant |
L |
4.8201218146388 |
L(r)(E,1)/r! |
Ω |
0.22050512901447 |
Real period |
R |
5.464863601538 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001295 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
68544do1 2142r1 22848bm1 |
Quadratic twists by: -4 8 -3 |