Properties

Label 2320.e
Number of curves $2$
Conductor $2320$
CM no
Rank $0$
Graph

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

Elliptic curves in class 2320.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2320.e1 2320f1 \([0, 0, 0, -43, -102]\) \(2146689/145\) \(593920\) \([2]\) \(256\) \(-0.14335\) \(\Gamma_0(N)\)-optimal
2320.e2 2320f2 \([0, 0, 0, 37, -438]\) \(1367631/21025\) \(-86118400\) \([2]\) \(512\) \(0.20322\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2320.e have rank \(0\).

Complex multiplication

The elliptic curves in class 2320.e do not have complex multiplication.

Modular form 2320.2.a.e

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.