Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 13860.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13860.r1 13860e1 \([0, 0, 0, -309312, -66212991]\) \(10392086293512192/1684375\) \(530456850000\) \([2]\) \(74880\) \(1.6517\) \(\Gamma_0(N)\)-optimal
13860.r2 13860e2 \([0, 0, 0, -308367, -66637674]\) \(-643570518871152/8271484375\) \(-41678752500000000\) \([2]\) \(149760\) \(1.9983\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 13860.2.a.r

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