Atkin-Lehner |
2+ 3- 31+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
69936f |
Isogeny class |
Conductor |
69936 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
30720 |
Modular degree for the optimal curve |
Δ |
-7188651504 = -1 · 24 · 38 · 31 · 472 |
Discriminant |
Eigenvalues |
2+ 3- -1 3 0 -4 0 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-656,-7869] |
[a1,a2,a3,a4,a6] |
Generators |
[37:141:1] |
Generators of the group modulo torsion |
j |
-1954236469504/449290719 |
j-invariant |
L |
8.0359674164736 |
L(r)(E,1)/r! |
Ω |
0.46592646716016 |
Real period |
R |
1.0779554263449 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999995343 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34968b1 |
Quadratic twists by: -4 |