Properties

Label 320.f
Number of curves 4
Conductor 320
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("320.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 320.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
320.f1 320c3 [0, -1, 0, -165, -763] [2] 48  
320.f2 320c4 [0, -1, 0, -145, -975] [2] 96  
320.f3 320c1 [0, -1, 0, -5, 5] [2] 16 \(\Gamma_0(N)\)-optimal
320.f4 320c2 [0, -1, 0, 15, 17] [2] 32  

Rank

sage: E.rank()
 

The elliptic curves in class 320.f have rank \(0\).

Modular form 320.2.a.f

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 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.