Properties

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

Related objects

Downloads

Learn more

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

Elliptic curves in class 3366k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3366.i1 3366k1 \([1, -1, 0, -8136, -278208]\) \(81706955619457/744505344\) \(542744395776\) \([2]\) \(8960\) \(1.0739\) \(\Gamma_0(N)\)-optimal
3366.i2 3366k2 \([1, -1, 0, -2376, -668736]\) \(-2035346265217/264305213568\) \(-192678500691072\) \([2]\) \(17920\) \(1.4204\)  

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)
 
\(q - q^{2} + q^{4} + 2 q^{5} - 4 q^{7} - q^{8} - 2 q^{10} + q^{11} - 4 q^{13} + 4 q^{14} + q^{16} + q^{17} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.