Properties

Label 3366k
Number of curves $2$
Conductor $3366$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3366k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3366.i1 3366k1 [1, -1, 0, -8136, -278208] [2] 8960 \(\Gamma_0(N)\)-optimal
3366.i2 3366k2 [1, -1, 0, -2376, -668736] [2] 17920  

Rank

sage: E.rank()
 

The elliptic curves in class 3366k have rank \(0\).

Complex multiplication

The elliptic curves in class 3366k do not have complex multiplication.

Modular form 3366.2.a.k

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} + 2q^{5} - 4q^{7} - q^{8} - 2q^{10} + q^{11} - 4q^{13} + 4q^{14} + q^{16} + q^{17} - 8q^{19} + O(q^{20}) \)

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.