Atkin-Lehner |
2+ 11- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
21472b |
Isogeny class |
Conductor |
21472 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
14976 |
Modular degree for the optimal curve |
Δ |
-20286058496 = -1 · 212 · 113 · 612 |
Discriminant |
Eigenvalues |
2+ -1 -3 -2 11- -4 -4 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-957,13621] |
[a1,a2,a3,a4,a6] |
Generators |
[12:61:1] [19:44:1] |
Generators of the group modulo torsion |
j |
-23689358848/4952651 |
j-invariant |
L |
5.1206923853838 |
L(r)(E,1)/r! |
Ω |
1.163233288499 |
Real period |
R |
0.36684332340543 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999996 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
21472c1 42944d1 |
Quadratic twists by: -4 8 |