Properties

Label 320.a
Number of curves $4$
Conductor $320$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 320.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
320.a1 320f3 \([0, 1, 0, -165, 763]\) \(488095744/125\) \(128000\) \([2]\) \(48\) \(-0.034070\)  
320.a2 320f4 \([0, 1, 0, -145, 975]\) \(-20720464/15625\) \(-256000000\) \([2]\) \(96\) \(0.31250\)  
320.a3 320f1 \([0, 1, 0, -5, -5]\) \(16384/5\) \(5120\) \([2]\) \(16\) \(-0.58338\) \(\Gamma_0(N)\)-optimal
320.a4 320f2 \([0, 1, 0, 15, -17]\) \(21296/25\) \(-409600\) \([2]\) \(32\) \(-0.23680\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 320.a do not have complex multiplication.

Modular form 320.2.a.a

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

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.