Atkin-Lehner |
3- 7- 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
99099bz |
Isogeny class |
Conductor |
99099 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
829440 |
Modular degree for the optimal curve |
Δ |
181176486962980509 = 321 · 7 · 114 · 132 |
Discriminant |
Eigenvalues |
0 3- -3 7- 11- 13- 3 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-173514,-18829143] |
[a1,a2,a3,a4,a6] |
Generators |
[-2414:19679:8] |
Generators of the group modulo torsion |
j |
54128875896832/16974756981 |
j-invariant |
L |
4.2159623516709 |
L(r)(E,1)/r! |
Ω |
0.23967953242605 |
Real period |
R |
2.1987496715539 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.00000000144 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
33033ba1 99099r1 |
Quadratic twists by: -3 -11 |