Atkin-Lehner |
2+ 3- 5- 7+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
78120m |
Isogeny class |
Conductor |
78120 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
442368 |
Modular degree for the optimal curve |
Δ |
-33372192792960000 = -1 · 210 · 36 · 54 · 74 · 313 |
Discriminant |
Eigenvalues |
2+ 3- 5- 7+ -2 0 2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,59973,6730054] |
[a1,a2,a3,a4,a6] |
Generators |
[63:3280:1] |
Generators of the group modulo torsion |
j |
31956819437084/44705119375 |
j-invariant |
L |
7.151017095721 |
L(r)(E,1)/r! |
Ω |
0.24923732258536 |
Real period |
R |
3.5864497644116 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001077 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
8680j1 |
Quadratic twists by: -3 |