Atkin-Lehner |
2- 3+ 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
6864q |
Isogeny class |
Conductor |
6864 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
13824 |
Modular degree for the optimal curve |
Δ |
-18473542483968 = -1 · 220 · 36 · 11 · 133 |
Discriminant |
Eigenvalues |
2- 3+ 0 4 11- 13- 0 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,5752,-122640] |
[a1,a2,a3,a4,a6] |
j |
5137417856375/4510142208 |
j-invariant |
L |
2.2733074912782 |
L(r)(E,1)/r! |
Ω |
0.3788845818797 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
858b1 27456by1 20592bf1 75504bh1 |
Quadratic twists by: -4 8 -3 -11 |