Atkin-Lehner |
3- 5+ 13- 73- |
Signs for the Atkin-Lehner involutions |
Class |
42705h |
Isogeny class |
Conductor |
42705 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
69120 |
Modular degree for the optimal curve |
Δ |
-28805610409875 = -1 · 39 · 53 · 133 · 732 |
Discriminant |
Eigenvalues |
0 3- 5+ -1 3 13- -3 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-3558,-270837] |
[a1,a2,a3,a4,a6] |
Generators |
[269:4270:1] [113:877:1] |
Generators of the group modulo torsion |
j |
-6833040818176/39513868875 |
j-invariant |
L |
7.4830967061877 |
L(r)(E,1)/r! |
Ω |
0.2770077909532 |
Real period |
R |
1.1255845729763 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999999 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
14235k1 |
Quadratic twists by: -3 |