Atkin-Lehner |
7- 17+ 43- |
Signs for the Atkin-Lehner involutions |
Class |
86989f |
Isogeny class |
Conductor |
86989 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
-90287228558863 = -1 · 7 · 178 · 432 |
Discriminant |
Eigenvalues |
1 0 0 7- -4 2 17+ -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,8038,361399] |
[a1,a2,a3,a4,a6] |
Generators |
[-878130880:12080202479:32768000] |
Generators of the group modulo torsion |
j |
2379270375/3740527 |
j-invariant |
L |
5.5204097196371 |
L(r)(E,1)/r! |
Ω |
0.41103064906033 |
Real period |
R |
13.430652255932 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000010104 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
5117b1 |
Quadratic twists by: 17 |