Atkin-Lehner |
2+ 31- 59- |
Signs for the Atkin-Lehner involutions |
Class |
117056i |
Isogeny class |
Conductor |
117056 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
2405376 |
Modular degree for the optimal curve |
Δ |
-1994918713064685568 = -1 · 245 · 312 · 59 |
Discriminant |
Eigenvalues |
2+ 2 0 -1 3 -5 -3 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-2574273,1592064449] |
[a1,a2,a3,a4,a6] |
Generators |
[1063431:22337360:729] |
Generators of the group modulo torsion |
j |
-7196938041625152625/7610010959872 |
j-invariant |
L |
9.3679665318496 |
L(r)(E,1)/r! |
Ω |
0.26101310683065 |
Real period |
R |
8.9726974113456 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000021246 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117056m1 3658d1 |
Quadratic twists by: -4 8 |