Atkin-Lehner |
2+ 3+ 5+ 7+ |
Signs for the Atkin-Lehner involutions |
Class |
47040a |
Isogeny class |
Conductor |
47040 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
322560 |
Modular degree for the optimal curve |
Δ |
-2176139510415360 = -1 · 223 · 32 · 5 · 78 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 7+ 1 -7 -4 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-112961,-14746815] |
[a1,a2,a3,a4,a6] |
Generators |
[2576:129543:1] |
Generators of the group modulo torsion |
j |
-105484561/1440 |
j-invariant |
L |
3.8392301203187 |
L(r)(E,1)/r! |
Ω |
0.13010213407265 |
Real period |
R |
7.3773388647302 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000012 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
47040fr1 1470r1 47040dg1 |
Quadratic twists by: -4 8 -7 |