Properties

Label 3360.k
Number of curves $4$
Conductor $3360$
CM no
Rank $1$
Graph

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

Elliptic curves in class 3360.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3360.k1 3360g3 \([0, -1, 0, -14120, 650532]\) \(608119035935048/826875\) \(423360000\) \([4]\) \(3072\) \(0.92955\)  
3360.k2 3360g2 \([0, -1, 0, -2240, -26520]\) \(2428799546888/778248135\) \(398463045120\) \([2]\) \(3072\) \(0.92955\)  
3360.k3 3360g1 \([0, -1, 0, -890, 10200]\) \(1219555693504/43758225\) \(2800526400\) \([2, 2]\) \(1536\) \(0.58297\) \(\Gamma_0(N)\)-optimal
3360.k4 3360g4 \([0, -1, 0, 335, 34945]\) \(1012048064/130203045\) \(-533311672320\) \([2]\) \(3072\) \(0.92955\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3360.k have rank \(1\).

Complex multiplication

The elliptic curves in class 3360.k do not have complex multiplication.

Modular form 3360.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{7} + q^{9} + 2q^{13} - q^{15} - 2q^{17} - 4q^{19} + O(q^{20})\)  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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.