Properties

Label 4410.k
Number of curves 4
Conductor 4410
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("4410.k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4410.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4410.k1 4410c4 [1, -1, 0, -56310, 5157116] [2] 17280  
4410.k2 4410c3 [1, -1, 0, -3390, 87380] [2] 8640  
4410.k3 4410c2 [1, -1, 0, -1185, -3809] [2] 5760  
4410.k4 4410c1 [1, -1, 0, 285, -575] [2] 2880 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4410.k have rank \(0\).

Modular form 4410.2.a.k

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} + 6q^{11} + 4q^{13} + q^{16} + 6q^{17} + 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.