Atkin-Lehner |
2- 5- 13- 83- |
Signs for the Atkin-Lehner involutions |
Class |
86320bh |
Isogeny class |
Conductor |
86320 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
12165120 |
Modular degree for the optimal curve |
Δ |
-603950018750000 = -1 · 24 · 58 · 132 · 833 |
Discriminant |
Eigenvalues |
2- -3 5- -3 3 13- -7 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-93018292,345303241051] |
[a1,a2,a3,a4,a6] |
Generators |
[45586:134875:8] |
Generators of the group modulo torsion |
j |
-5562996820181617138466144256/37746876171875 |
j-invariant |
L |
2.4635278063119 |
L(r)(E,1)/r! |
Ω |
0.25241487586062 |
Real period |
R |
0.20332991835527 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999735865 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
21580f1 |
Quadratic twists by: -4 |