Atkin-Lehner |
3- 5+ 11+ 83- |
Signs for the Atkin-Lehner involutions |
Class |
68475f |
Isogeny class |
Conductor |
68475 |
Conductor |
∏ cp |
3 |
Product of Tamagawa factors cp |
deg |
120960 |
Modular degree for the optimal curve |
Δ |
-46605796875 = -1 · 33 · 56 · 113 · 83 |
Discriminant |
Eigenvalues |
-2 3- 5+ 0 11+ 6 -5 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-3008,-65356] |
[a1,a2,a3,a4,a6] |
Generators |
[64:91:1] |
Generators of the group modulo torsion |
j |
-192699928576/2982771 |
j-invariant |
L |
3.7028690430636 |
L(r)(E,1)/r! |
Ω |
0.32202428334338 |
Real period |
R |
3.8329087099034 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000004812 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
2739b1 |
Quadratic twists by: 5 |