Atkin-Lehner |
2+ 3- 5- 7+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
21840r |
Isogeny class |
Conductor |
21840 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
27648 |
Modular degree for the optimal curve |
Δ |
-1547556192000 = -1 · 28 · 312 · 53 · 7 · 13 |
Discriminant |
Eigenvalues |
2+ 3- 5- 7+ 0 13+ -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,2820,17100] |
[a1,a2,a3,a4,a6] |
Generators |
[30:360:1] |
Generators of the group modulo torsion |
j |
9684496745264/6045141375 |
j-invariant |
L |
6.5957755794213 |
L(r)(E,1)/r! |
Ω |
0.52451748161523 |
Real period |
R |
0.69860774803178 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
10920f1 87360eg1 65520m1 109200s1 |
Quadratic twists by: -4 8 -3 5 |