Atkin-Lehner |
2+ 3- 31- |
Signs for the Atkin-Lehner involutions |
Class |
69192r |
Isogeny class |
Conductor |
69192 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
61440 |
Modular degree for the optimal curve |
Δ |
-347482224 = -1 · 24 · 36 · 313 |
Discriminant |
Eigenvalues |
2+ 3- 3 1 -4 2 6 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-6231,-189317] |
[a1,a2,a3,a4,a6] |
Generators |
[227:3177:1] |
Generators of the group modulo torsion |
j |
-76995328 |
j-invariant |
L |
8.9474132400381 |
L(r)(E,1)/r! |
Ω |
0.26867656222596 |
Real period |
R |
4.162725046499 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000174 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
7688p1 69192q1 |
Quadratic twists by: -3 -31 |