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Properties

Label 13650.e
Number of curves $2$
Conductor $13650$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 13650.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13650.e1 13650o1 \([1, 1, 0, -217450, 38876500]\) \(582203792000501/1069915392\) \(2089678500000000\) \([2]\) \(122880\) \(1.8309\) \(\Gamma_0(N)\)-optimal
13650.e2 13650o2 \([1, 1, 0, -147450, 64426500]\) \(-181523395171061/814788335088\) \(-1591383466968750000\) \([2]\) \(245760\) \(2.1774\)  

Rank

sage: E.rank()
 

The elliptic curves in class 13650.e have rank \(1\).

Complex multiplication

The elliptic curves in class 13650.e do not have complex multiplication.

Modular form 13650.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{7} - q^{8} + q^{9} - q^{12} + q^{13} + q^{14} + q^{16} - 2 q^{17} - q^{18} - 6 q^{19} + O(q^{20})\) Copy content 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.