Atkin-Lehner |
2+ 3- 31- |
Signs for the Atkin-Lehner involutions |
Class |
69192m |
Isogeny class |
Conductor |
69192 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
368640 |
Modular degree for the optimal curve |
Δ |
-20538056383405056 = -1 · 210 · 36 · 317 |
Discriminant |
Eigenvalues |
2+ 3- -2 0 2 -4 6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,66309,-2085370] |
[a1,a2,a3,a4,a6] |
Generators |
[164362:3761354:1331] |
Generators of the group modulo torsion |
j |
48668/31 |
j-invariant |
L |
5.5312782225351 |
L(r)(E,1)/r! |
Ω |
0.22019861007257 |
Real period |
R |
6.2798741333704 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000253 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
7688l1 2232c1 |
Quadratic twists by: -3 -31 |