Atkin-Lehner |
2- 3- 7+ 13+ 61- |
Signs for the Atkin-Lehner involutions |
Class |
33306r |
Isogeny class |
Conductor |
33306 |
Conductor |
∏ cp |
308 |
Product of Tamagawa factors cp |
deg |
113344 |
Modular degree for the optimal curve |
Δ |
-2262514415616 = -1 · 211 · 37 · 72 · 132 · 61 |
Discriminant |
Eigenvalues |
2- 3- -3 7+ -6 13+ -3 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-3987,120609] |
[a1,a2,a3,a4,a6] |
Generators |
[12:-279:1] [-66:345:1] |
Generators of the group modulo torsion |
j |
-7009212504499633/2262514415616 |
j-invariant |
L |
11.755420616183 |
L(r)(E,1)/r! |
Ω |
0.77522904075936 |
Real period |
R |
0.049233127302803 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000002 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
99918g1 |
Quadratic twists by: -3 |