Properties

Label 441d
Number of curves 4
Conductor 441
CM -7
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("441.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 441d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
441.c4 441d1 [1, -1, 1, -20, 46] [2] 32 \(\Gamma_0(N)\)-optimal
441.c3 441d2 [1, -1, 1, -335, 2440] [2] 64  
441.c2 441d3 [1, -1, 1, -965, -13940] [2] 224  
441.c1 441d4 [1, -1, 1, -16400, -804212] [2] 448  

Rank

sage: E.rank()
 

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

Modular form 441.2.a.c

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{4} + 3q^{8} - 4q^{11} - q^{16} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 7 & 14 \\ 2 & 1 & 14 & 7 \\ 7 & 14 & 1 & 2 \\ 14 & 7 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.