Atkin-Lehner |
2- 3+ 11- 43+ |
Signs for the Atkin-Lehner involutions |
Class |
68112bg |
Isogeny class |
Conductor |
68112 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
Δ |
-18024274224 = -1 · 24 · 39 · 113 · 43 |
Discriminant |
Eigenvalues |
2- 3+ 3 1 11- -4 3 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-5076,139347] |
[a1,a2,a3,a4,a6] |
Generators |
[354:297:8] |
Generators of the group modulo torsion |
j |
-45927972864/57233 |
j-invariant |
L |
8.6633001190904 |
L(r)(E,1)/r! |
Ω |
1.223855523003 |
Real period |
R |
1.179782520061 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000434 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
17028b2 68112bb1 |
Quadratic twists by: -4 -3 |