Properties

Label 320e
Number of curves $2$
Conductor $320$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 320e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
320.b2 320e1 \([0, 1, 0, 0, -2]\) \(-64/25\) \(-1600\) \([2]\) \(16\) \(-0.70605\) \(\Gamma_0(N)\)-optimal
320.b1 320e2 \([0, 1, 0, -25, -57]\) \(438976/5\) \(20480\) \([2]\) \(32\) \(-0.35947\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 320.2.a.e

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