Properties

Label 441f
Number of curves 2
Conductor 441
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("441.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 441f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
441.a2 441f1 [0, 0, 1, -21, 40] [] 48 \(\Gamma_0(N)\)-optimal
441.a1 441f2 [0, 0, 1, -8211, -286610] [] 624  

Rank

sage: E.rank()
 

The elliptic curves in class 441f have rank \(1\).

Modular form 441.2.a.a

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

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.

\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.