Atkin-Lehner |
2- 3+ 7+ 11- |
Signs for the Atkin-Lehner involutions |
Class |
121968co |
Isogeny class |
Conductor |
121968 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
677376 |
Modular degree for the optimal curve |
Δ |
-71088367730688 = -1 · 219 · 33 · 73 · 114 |
Discriminant |
Eigenvalues |
2- 3+ 0 7+ 11- 5 -6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-415635,-103138222] |
[a1,a2,a3,a4,a6] |
Generators |
[386911:10078272:343] |
Generators of the group modulo torsion |
j |
-4904170882875/43904 |
j-invariant |
L |
6.0594414564897 |
L(r)(E,1)/r! |
Ω |
0.094013733058075 |
Real period |
R |
8.0565908292477 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000032771 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
15246c1 121968cn2 121968cz1 |
Quadratic twists by: -4 -3 -11 |