Properties

Label 13860.d
Number of curves $2$
Conductor $13860$
CM no
Rank $0$
Graph

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

Elliptic curves in class 13860.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13860.d1 13860k2 \([0, 0, 0, -423, -2322]\) \(44851536/13475\) \(2514758400\) \([2]\) \(6144\) \(0.50907\)  
13860.d2 13860k1 \([0, 0, 0, 72, -243]\) \(3538944/4235\) \(-49397040\) \([2]\) \(3072\) \(0.16250\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 13860.d have rank \(0\).

Complex multiplication

The elliptic curves in class 13860.d do not have complex multiplication.

Modular form 13860.2.a.d

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