Atkin-Lehner |
13+ 79- |
Signs for the Atkin-Lehner involutions |
Class |
81133b |
Isogeny class |
Conductor |
81133 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
3185280 |
Modular degree for the optimal curve |
Δ |
-2.6331395637381E+20 |
Discriminant |
Eigenvalues |
-2 0 -2 -3 -4 13+ 6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,493039,-769264100] |
[a1,a2,a3,a4,a6] |
Generators |
[12482:493035:8] [26785:4385084:1] |
Generators of the group modulo torsion |
j |
110592/2197 |
j-invariant |
L |
3.7272587096911 |
L(r)(E,1)/r! |
Ω |
0.084848927190446 |
Real period |
R |
21.964088605342 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999998194 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
81133a1 |
Quadratic twists by: -79 |