Atkin-Lehner |
2- 7+ 11- 41+ |
Signs for the Atkin-Lehner involutions |
Class |
69454n |
Isogeny class |
Conductor |
69454 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
Δ |
-135822616078471168 = -1 · 212 · 73 · 119 · 41 |
Discriminant |
Eigenvalues |
2- -2 0 7+ 11- -2 6 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,110047,10824265] |
[a1,a2,a3,a4,a6] |
Generators |
[714:20939:1] |
Generators of the group modulo torsion |
j |
83195910236375/76668325888 |
j-invariant |
L |
6.3683499100139 |
L(r)(E,1)/r! |
Ω |
0.21446840999117 |
Real period |
R |
0.61861770909032 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999998223 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
6314d2 |
Quadratic twists by: -11 |