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Properties

Label 41650.f
Number of curves $4$
Conductor $41650$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 41650.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
41650.f1 41650n4 [1, 0, 1, -138451, 13690548] [2] 497664  
41650.f2 41650n3 [1, 0, 1, -126201, 17243048] [2] 248832  
41650.f3 41650n2 [1, 0, 1, -52701, -4659952] [2] 165888  
41650.f4 41650n1 [1, 0, 1, -3701, -53952] [2] 82944 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 41650.f have rank \(0\).

Complex multiplication

The elliptic curves in class 41650.f do not have complex multiplication.

Modular form 41650.2.a.f

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.