Atkin-Lehner |
7- 29+ 41+ |
Signs for the Atkin-Lehner involutions |
Class |
8323c |
Isogeny class |
Conductor |
8323 |
Conductor |
∏ cp |
3 |
Product of Tamagawa factors cp |
deg |
1212 |
Modular degree for the optimal curve |
Δ |
-407827 = -1 · 73 · 29 · 41 |
Discriminant |
Eigenvalues |
0 -2 0 7- 3 2 -6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-243,1380] |
[a1,a2,a3,a4,a6] |
j |
-1593413632000/407827 |
j-invariant |
L |
0.97335212831601 |
L(r)(E,1)/r! |
Ω |
2.920056384948 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
74907j1 58261h1 |
Quadratic twists by: -3 -7 |