Atkin-Lehner |
2+ 3- 13+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
36192q |
Isogeny class |
Conductor |
36192 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
225792 |
Modular degree for the optimal curve |
Δ |
-3778934560567296 = -1 · 212 · 3 · 139 · 29 |
Discriminant |
Eigenvalues |
2+ 3- -3 4 2 13+ -3 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,33043,-1833669] |
[a1,a2,a3,a4,a6] |
Generators |
[48789279:3093060996:12167] |
Generators of the group modulo torsion |
j |
974067452145152/922591445451 |
j-invariant |
L |
6.5456590634462 |
L(r)(E,1)/r! |
Ω |
0.2415454315575 |
Real period |
R |
13.549540186373 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999998 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
36192h1 72384cj1 108576bg1 |
Quadratic twists by: -4 8 -3 |