Atkin-Lehner |
2- 3+ 5- 7+ |
Signs for the Atkin-Lehner involutions |
Class |
47040et |
Isogeny class |
Conductor |
47040 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
322560 |
Modular degree for the optimal curve |
Δ |
-23786174640291840 = -1 · 225 · 310 · 5 · 74 |
Discriminant |
Eigenvalues |
2- 3+ 5- 7+ -1 -1 0 -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-39265,-7988735] |
[a1,a2,a3,a4,a6] |
Generators |
[1447:54432:1] |
Generators of the group modulo torsion |
j |
-10637008249/37791360 |
j-invariant |
L |
4.9171434380333 |
L(r)(E,1)/r! |
Ω |
0.15558624450179 |
Real period |
R |
2.633664399324 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000013 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
47040cv1 11760cb1 47040fw1 |
Quadratic twists by: -4 8 -7 |