Properties

Label 1650.k
Number of curves $4$
Conductor $1650$
CM no
Rank $0$
Graph

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

Elliptic curves in class 1650.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1650.k1 1650f3 [1, 0, 1, -8801, -318502] [2] 2048  
1650.k2 1650f2 [1, 0, 1, -551, -5002] [2, 2] 1024  
1650.k3 1650f4 [1, 0, 1, -301, -9502] [2] 2048  
1650.k4 1650f1 [1, 0, 1, -51, -2] [2] 512 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1650.k have rank \(0\).

Complex multiplication

The elliptic curves in class 1650.k do not have complex multiplication.

Modular form 1650.2.a.k

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} - q^{6} + 4q^{7} - q^{8} + q^{9} - q^{11} + q^{12} + 6q^{13} - 4q^{14} + q^{16} - 2q^{17} - q^{18} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.