Properties

Label 320f
Number of curves 4
Conductor 320
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("320.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 320f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
320.a3 320f1 [0, 1, 0, -5, -5] [2] 16 \(\Gamma_0(N)\)-optimal
320.a4 320f2 [0, 1, 0, 15, -17] [2] 32  
320.a1 320f3 [0, 1, 0, -165, 763] [2] 48  
320.a2 320f4 [0, 1, 0, -145, 975] [2] 96  

Rank

sage: E.rank()
 

The elliptic curves in class 320f have rank \(1\).

Modular form 320.2.a.a

sage: E.q_eigenform(10)
 
\( q - 2q^{3} + q^{5} - 2q^{7} + q^{9} - 2q^{13} - 2q^{15} - 6q^{17} - 4q^{19} + O(q^{20}) \)

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 Cremona 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 Cremona labels.