Properties

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

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 2320.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2320.d1 2320e1 \([0, 0, 0, -1123, 14178]\) \(38238692409/928000\) \(3801088000\) \([2]\) \(1152\) \(0.62252\) \(\Gamma_0(N)\)-optimal
2320.d2 2320e2 \([0, 0, 0, 157, 44642]\) \(104487111/210250000\) \(-861184000000\) \([2]\) \(2304\) \(0.96909\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2320.2.a.d

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