Properties

Label 23520.a
Number of curves $2$
Conductor $23520$
CM no
Rank $1$
Graph

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

Elliptic curves in class 23520.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23520.a1 23520bi1 \([0, -1, 0, -67146, -6674604]\) \(4446542056384/25725\) \(193697313600\) \([2]\) \(92160\) \(1.3561\) \(\Gamma_0(N)\)-optimal
23520.a2 23520bi2 \([0, -1, 0, -65921, -6931119]\) \(-65743598656/5294205\) \(-2551226056888320\) \([2]\) \(184320\) \(1.7027\)  

Rank

sage: E.rank()
 

The elliptic curves in class 23520.a have rank \(1\).

Complex multiplication

The elliptic curves in class 23520.a do not have complex multiplication.

Modular form 23520.2.a.a

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