Atkin-Lehner |
2- 3+ 7+ 11- |
Signs for the Atkin-Lehner involutions |
Class |
121968cp |
Isogeny class |
Conductor |
121968 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
3346036936704 = 212 · 39 · 73 · 112 |
Discriminant |
Eigenvalues |
2- 3+ 1 7+ 11- -4 -1 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-4752,90288] |
[a1,a2,a3,a4,a6] |
Generators |
[-606:999:8] |
Generators of the group modulo torsion |
j |
1216512/343 |
j-invariant |
L |
6.6113044296121 |
L(r)(E,1)/r! |
Ω |
0.73947980514167 |
Real period |
R |
4.4702399919066 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000050382 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
7623c1 121968cq1 121968db1 |
Quadratic twists by: -4 -3 -11 |