Atkin-Lehner |
2+ 3- 5- 13+ 59+ |
Signs for the Atkin-Lehner involutions |
Class |
69030r |
Isogeny class |
Conductor |
69030 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
18432 |
Modular degree for the optimal curve |
Δ |
-44731440 = -1 · 24 · 36 · 5 · 13 · 59 |
Discriminant |
Eigenvalues |
2+ 3- 5- -1 3 13+ 2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,36,-320] |
[a1,a2,a3,a4,a6] |
Generators |
[20:80:1] |
Generators of the group modulo torsion |
j |
6967871/61360 |
j-invariant |
L |
5.6162374277515 |
L(r)(E,1)/r! |
Ω |
1.0015805191616 |
Real period |
R |
1.4018437159989 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.00000000006 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
7670g1 |
Quadratic twists by: -3 |