Atkin-Lehner |
2- 3- 31- 47- |
Signs for the Atkin-Lehner involutions |
Class |
69936bb |
Isogeny class |
Conductor |
69936 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
107136 |
Modular degree for the optimal curve |
Δ |
137642999808 = 215 · 3 · 313 · 47 |
Discriminant |
Eigenvalues |
2- 3- 2 0 0 2 5 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-18632,-984972] |
[a1,a2,a3,a4,a6] |
Generators |
[-9930:1488:125] |
Generators of the group modulo torsion |
j |
174648757219273/33604248 |
j-invariant |
L |
9.8566345461312 |
L(r)(E,1)/r! |
Ω |
0.40863706637225 |
Real period |
R |
2.0100629135429 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999999559 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8742a1 |
Quadratic twists by: -4 |