Properties

Label 441.d
Number of curves $2$
Conductor $441$
CM -3
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("441.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 441.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
441.d1 441b2 [0, 0, 1, 0, -331] [] 72  
441.d2 441b1 [0, 0, 1, 0, 12] [3] 24 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 441.2.a.d

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

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.