Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 13860.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13860.n1 13860d1 \([0, 0, 0, -48, 117]\) \(28311552/2695\) \(1164240\) \([2]\) \(2688\) \(-0.098164\) \(\Gamma_0(N)\)-optimal
13860.n2 13860d2 \([0, 0, 0, 57, 558]\) \(2963088/21175\) \(-146361600\) \([2]\) \(5376\) \(0.24841\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 13860.2.a.n

sage: E.q_eigenform(10)
 
\(q - q^{5} + q^{7} + q^{11} + 6q^{13} + 2q^{17} + 8q^{19} + O(q^{20})\)  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.