Atkin-Lehner |
2+ 3- 5- 23- 41- |
Signs for the Atkin-Lehner involutions |
Class |
84870t |
Isogeny class |
Conductor |
84870 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
983040 |
Modular degree for the optimal curve |
Δ |
3557538225000000 = 26 · 38 · 58 · 232 · 41 |
Discriminant |
Eigenvalues |
2+ 3- 5- 4 2 -4 0 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-345069,78053733] |
[a1,a2,a3,a4,a6] |
Generators |
[322:339:1] |
Generators of the group modulo torsion |
j |
6233252610858963409/4880025000000 |
j-invariant |
L |
6.3334257304261 |
L(r)(E,1)/r! |
Ω |
0.4407972293157 |
Real period |
R |
0.89800725140575 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999956186 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
28290s1 |
Quadratic twists by: -3 |