Atkin-Lehner |
2+ 3+ 5- 71+ |
Signs for the Atkin-Lehner involutions |
Class |
8520f |
Isogeny class |
Conductor |
8520 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
3072 |
Modular degree for the optimal curve |
Δ |
-20448000 = -1 · 28 · 32 · 53 · 71 |
Discriminant |
Eigenvalues |
2+ 3+ 5- -3 -6 -3 -6 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-145,757] |
[a1,a2,a3,a4,a6] |
Generators |
[-11:30:1] [17:-54:1] |
Generators of the group modulo torsion |
j |
-1326109696/79875 |
j-invariant |
L |
4.8283577846097 |
L(r)(E,1)/r! |
Ω |
2.1285647022666 |
Real period |
R |
0.094515132260029 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999991 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
17040j1 68160y1 25560f1 42600bd1 |
Quadratic twists by: -4 8 -3 5 |