Atkin-Lehner |
2- 31+ 43+ |
Signs for the Atkin-Lehner involutions |
Class |
85312o |
Isogeny class |
Conductor |
85312 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
23040 |
Modular degree for the optimal curve |
Δ |
43679744 = 215 · 31 · 43 |
Discriminant |
Eigenvalues |
2- -2 -3 2 1 1 -4 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-257,1471] |
[a1,a2,a3,a4,a6] |
Generators |
[-9:56:1] [7:8:1] |
Generators of the group modulo torsion |
j |
57512456/1333 |
j-invariant |
L |
7.1127328874483 |
L(r)(E,1)/r! |
Ω |
2.024206548768 |
Real period |
R |
0.87845937602849 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000442 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
85312y1 42656e1 |
Quadratic twists by: -4 8 |