Atkin-Lehner |
3+ 7+ 13- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
8463a |
Isogeny class |
Conductor |
8463 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
2176 |
Modular degree for the optimal curve |
Δ |
55779633 = 32 · 7 · 134 · 31 |
Discriminant |
Eigenvalues |
-1 3+ 2 7+ -4 13- 2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-97,38] |
[a1,a2,a3,a4,a6] |
j |
100999381393/55779633 |
j-invariant |
L |
0.8621184135223 |
L(r)(E,1)/r! |
Ω |
1.7242368270446 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
25389e1 59241u1 110019n1 |
Quadratic twists by: -3 -7 13 |