Atkin-Lehner |
2+ 3+ 7- 11- |
Signs for the Atkin-Lehner involutions |
Class |
121968q |
Isogeny class |
Conductor |
121968 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
24576 |
Modular degree for the optimal curve |
Δ |
5854464 = 28 · 33 · 7 · 112 |
Discriminant |
Eigenvalues |
2+ 3+ 1 7- 11- -4 3 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-132,572] |
[a1,a2,a3,a4,a6] |
Generators |
[1:21:1] |
Generators of the group modulo torsion |
j |
304128/7 |
j-invariant |
L |
8.3987711503165 |
L(r)(E,1)/r! |
Ω |
2.3934261183491 |
Real period |
R |
1.7545499226704 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999149676 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
60984e1 121968t1 121968e1 |
Quadratic twists by: -4 -3 -11 |