Atkin-Lehner |
2+ 7+ 43- |
Signs for the Atkin-Lehner involutions |
Class |
33712b |
Isogeny class |
Conductor |
33712 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
8448 |
Modular degree for the optimal curve |
Δ |
71031184 = 24 · 74 · 432 |
Discriminant |
Eigenvalues |
2+ -1 -3 7+ -3 -2 3 -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-212,-1049] |
[a1,a2,a3,a4,a6] |
Generators |
[-9:7:1] [47:301:1] |
Generators of the group modulo torsion |
j |
27559168/1849 |
j-invariant |
L |
5.8611220231984 |
L(r)(E,1)/r! |
Ω |
1.2559508689468 |
Real period |
R |
0.77778016217485 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999999 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
16856a1 33712g1 |
Quadratic twists by: -4 -7 |