Atkin-Lehner |
2+ 3- 7- 67+ |
Signs for the Atkin-Lehner involutions |
Class |
33768g |
Isogeny class |
Conductor |
33768 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
12800 |
Modular degree for the optimal curve |
Δ |
-1329311088 = -1 · 24 · 311 · 7 · 67 |
Discriminant |
Eigenvalues |
2+ 3- -2 7- 3 -3 -6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-111,1811] |
[a1,a2,a3,a4,a6] |
Generators |
[19:81:1] |
Generators of the group modulo torsion |
j |
-12967168/113967 |
j-invariant |
L |
4.9144867817977 |
L(r)(E,1)/r! |
Ω |
1.3044378648866 |
Real period |
R |
0.47093914111277 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
67536p1 11256d1 |
Quadratic twists by: -4 -3 |