Properties

Label 13923l
Number of curves $2$
Conductor $13923$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 13923l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13923.k1 13923l1 \([1, -1, 0, -4095, -99792]\) \(10418796526321/6390657\) \(4658788953\) \([2]\) \(17920\) \(0.79795\) \(\Gamma_0(N)\)-optimal
13923.k2 13923l2 \([1, -1, 0, -3330, -138807]\) \(-5602762882081/8312741073\) \(-6059988242217\) \([2]\) \(35840\) \(1.1445\)  

Rank

sage: E.rank()
 

The elliptic curves in class 13923l have rank \(0\).

Complex multiplication

The elliptic curves in class 13923l do not have complex multiplication.

Modular form 13923.2.a.l

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} + 4q^{5} + q^{7} - 3q^{8} + 4q^{10} + 4q^{11} + q^{13} + q^{14} - q^{16} - q^{17} + O(q^{20})\)  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 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.