Atkin-Lehner |
3- 5- 13+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
30225be |
Isogeny class |
Conductor |
30225 |
Conductor |
∏ cp |
162 |
Product of Tamagawa factors cp |
deg |
401760 |
Modular degree for the optimal curve |
Δ |
-38709994826953125 = -1 · 39 · 58 · 132 · 313 |
Discriminant |
Eigenvalues |
-1 3- 5- -4 -4 13+ -1 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-1010263,390871142] |
[a1,a2,a3,a4,a6] |
Generators |
[-1123:11024:1] [1202:-30826:1] |
Generators of the group modulo torsion |
j |
-291922148818393105/99097586757 |
j-invariant |
L |
5.7468666335992 |
L(r)(E,1)/r! |
Ω |
0.35700649992653 |
Real period |
R |
0.099366497248344 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999993 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
90675bt1 30225j1 |
Quadratic twists by: -3 5 |