Properties

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

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 13650s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13650.q1 13650s1 \([1, 1, 0, -2778575, -1589302875]\) \(1214675547724509317/145065854029824\) \(283331746152000000000\) \([2]\) \(506880\) \(2.6554\) \(\Gamma_0(N)\)-optimal
13650.q2 13650s2 \([1, 1, 0, 3981425, -8112702875]\) \(3573626171578090363/16631459495816256\) \(-32483319327766125000000\) \([2]\) \(1013760\) \(3.0020\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 13650.2.a.s

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} + q^{7} - q^{8} + q^{9} - 2 q^{11} - q^{12} - q^{13} - q^{14} + q^{16} + 4 q^{17} - q^{18} - 2 q^{19} + O(q^{20})\) 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 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.