Atkin-Lehner |
2+ 3- 5+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
121680r |
Isogeny class |
Conductor |
121680 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
-306563512320 = -1 · 211 · 311 · 5 · 132 |
Discriminant |
Eigenvalues |
2+ 3- 5+ 2 -1 13+ -6 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1443,-33982] |
[a1,a2,a3,a4,a6] |
Generators |
[53:196:1] [61:324:1] |
Generators of the group modulo torsion |
j |
-1316978/1215 |
j-invariant |
L |
11.937445679171 |
L(r)(E,1)/r! |
Ω |
0.37310774357159 |
Real period |
R |
1.9996646214061 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000002083 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
60840k1 40560j1 121680bm1 |
Quadratic twists by: -4 -3 13 |