Atkin-Lehner |
2- 13+ 103- |
Signs for the Atkin-Lehner involutions |
Class |
85696bq |
Isogeny class |
Conductor |
85696 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
43008 |
Modular degree for the optimal curve |
Δ |
-4563140608 = -1 · 218 · 132 · 103 |
Discriminant |
Eigenvalues |
2- 0 0 4 6 13+ 6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-140,-3312] |
[a1,a2,a3,a4,a6] |
Generators |
[106612:940576:1331] |
Generators of the group modulo torsion |
j |
-1157625/17407 |
j-invariant |
L |
8.6373708095222 |
L(r)(E,1)/r! |
Ω |
0.58971186225317 |
Real period |
R |
7.3233822834086 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000973 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
85696a1 21424r1 |
Quadratic twists by: -4 8 |