Atkin-Lehner |
3+ 7+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
33327d |
Isogeny class |
Conductor |
33327 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
413952 |
Modular degree for the optimal curve |
Δ |
-75708544403665467 = -1 · 33 · 77 · 237 |
Discriminant |
Eigenvalues |
-2 3+ 2 7+ 1 0 4 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-201549,-37258396] |
[a1,a2,a3,a4,a6] |
j |
-226534772736/18941489 |
j-invariant |
L |
0.89700016971059 |
L(r)(E,1)/r! |
Ω |
0.11212502121367 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
33327c1 1449b1 |
Quadratic twists by: -3 -23 |