Atkin-Lehner |
2- 3- 5+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
12480cm |
Isogeny class |
Conductor |
12480 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
-1073234313216000000 = -1 · 228 · 39 · 56 · 13 |
Discriminant |
Eigenvalues |
2- 3- 5+ -2 0 13+ 0 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,255839,-1791265] |
[a1,a2,a3,a4,a6] |
Generators |
[257:9000:1] |
Generators of the group modulo torsion |
j |
7064514799444439/4094064000000 |
j-invariant |
L |
4.9253363035661 |
L(r)(E,1)/r! |
Ω |
0.16404388633365 |
Real period |
R |
1.6680279939603 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
12480b1 3120s1 37440fb1 62400ev1 |
Quadratic twists by: -4 8 -3 5 |