Atkin-Lehner |
3- 5+ 11- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
85305t |
Isogeny class |
Conductor |
85305 |
Conductor |
∏ cp |
14 |
Product of Tamagawa factors cp |
deg |
241920 |
Modular degree for the optimal curve |
Δ |
-121459658203125 = -1 · 37 · 510 · 112 · 47 |
Discriminant |
Eigenvalues |
1 3- 5+ 4 11- 0 -4 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-5019,-548033] |
[a1,a2,a3,a4,a6] |
Generators |
[7604:43041:64] |
Generators of the group modulo torsion |
j |
-115522222592689/1003798828125 |
j-invariant |
L |
10.41467201915 |
L(r)(E,1)/r! |
Ω |
0.24874993875997 |
Real period |
R |
2.990574179023 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000004515 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
85305u1 |
Quadratic twists by: -11 |