Atkin-Lehner |
2+ 3+ 13+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
36192c |
Isogeny class |
Conductor |
36192 |
Conductor |
∏ cp |
10 |
Product of Tamagawa factors cp |
deg |
1297920 |
Modular degree for the optimal curve |
Δ |
-1741283966536298496 = -1 · 212 · 313 · 13 · 295 |
Discriminant |
Eigenvalues |
2+ 3+ 1 4 -2 13+ 5 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-4971565,4268787589] |
[a1,a2,a3,a4,a6] |
j |
-3317746634020925825536/425118155892651 |
j-invariant |
L |
2.553745678997 |
L(r)(E,1)/r! |
Ω |
0.25537456789772 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
36192l1 72384dk1 108576w1 |
Quadratic twists by: -4 8 -3 |