Properties

Label 320.b
Number of curves 2
Conductor 320
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("320.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 320.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
320.b1 320e2 [0, 1, 0, -25, -57] [2] 32  
320.b2 320e1 [0, 1, 0, 0, -2] [2] 16 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 320.2.a.b

sage: E.q_eigenform(10)
 
\( q - 2q^{3} + q^{5} + 2q^{7} + q^{9} - 4q^{11} + 6q^{13} - 2q^{15} + 2q^{17} + 8q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.