Atkin-Lehner |
3- 11+ 17+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
31977m |
Isogeny class |
Conductor |
31977 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
196608 |
Modular degree for the optimal curve |
Δ |
-519488286480603 = -1 · 310 · 11 · 17 · 196 |
Discriminant |
Eigenvalues |
-2 3- -2 -3 11+ -2 17+ 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-19281,-1504800] |
[a1,a2,a3,a4,a6] |
Generators |
[200:1624:1] |
Generators of the group modulo torsion |
j |
-1087388780474368/712603959507 |
j-invariant |
L |
1.5039035417161 |
L(r)(E,1)/r! |
Ω |
0.196790697818 |
Real period |
R |
0.63684562600062 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
10659o1 |
Quadratic twists by: -3 |