Atkin-Lehner |
3- 13- 23+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
83421m |
Isogeny class |
Conductor |
83421 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1824768 |
Modular degree for the optimal curve |
Δ |
7910731138093141059 = 317 · 132 · 233 · 313 |
Discriminant |
Eigenvalues |
-1 3- 1 -1 5 13- 4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-3944417,3013190862] |
[a1,a2,a3,a4,a6] |
Generators |
[8158:52779:8] |
Generators of the group modulo torsion |
j |
9309889927492712263369/10851483042651771 |
j-invariant |
L |
4.505418583941 |
L(r)(E,1)/r! |
Ω |
0.23294327194709 |
Real period |
R |
2.4176586787996 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999982557 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
27807g1 |
Quadratic twists by: -3 |