Atkin-Lehner |
2- 3- 13+ 23+ |
Signs for the Atkin-Lehner involutions |
Class |
69966ba |
Isogeny class |
Conductor |
69966 |
Conductor |
∏ cp |
136 |
Product of Tamagawa factors cp |
deg |
1370880 |
Modular degree for the optimal curve |
Δ |
-3171732795476803584 = -1 · 217 · 36 · 137 · 232 |
Discriminant |
Eigenvalues |
2- 3- -1 1 -6 13+ -3 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,6052,85683615] |
[a1,a2,a3,a4,a6] |
Generators |
[1557:-62971:1] |
Generators of the group modulo torsion |
j |
6967871/901382144 |
j-invariant |
L |
8.3517759265849 |
L(r)(E,1)/r! |
Ω |
0.19970372433764 |
Real period |
R |
0.30750611837389 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000185 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
7774b1 5382c1 |
Quadratic twists by: -3 13 |