Properties

Label 20216.h
Number of curves $4$
Conductor $20216$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 20216.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
20216.h1 20216b3 [0, 0, 0, -107939, -13649410] [2] 48384  
20216.h2 20216b4 [0, 0, 0, -21299, 946542] [2] 48384  
20216.h3 20216b2 [0, 0, 0, -6859, -205770] [2, 2] 24192  
20216.h4 20216b1 [0, 0, 0, 361, -13718] [2] 12096 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 20216.h have rank \(0\).

Complex multiplication

The elliptic curves in class 20216.h do not have complex multiplication.

Modular form 20216.2.a.h

sage: E.q_eigenform(10)
 
\( q + 2q^{5} - q^{7} - 3q^{9} - 4q^{11} - 2q^{13} - 6q^{17} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.