Atkin-Lehner |
3+ 7+ 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
33033j |
Isogeny class |
Conductor |
33033 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
786240 |
Modular degree for the optimal curve |
Δ |
-1592774370184544547 = -1 · 3 · 7 · 1113 · 133 |
Discriminant |
Eigenvalues |
2 3+ 0 7+ 11- 13- 6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,227682,43951577] |
[a1,a2,a3,a4,a6] |
Generators |
[218440:7569141:512] |
Generators of the group modulo torsion |
j |
736803680768000/899079608427 |
j-invariant |
L |
9.2183720443189 |
L(r)(E,1)/r! |
Ω |
0.17886473175593 |
Real period |
R |
4.2948526678148 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999998 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
99099bj1 3003f1 |
Quadratic twists by: -3 -11 |