Properties

Label 234650n
Number of curves $4$
Conductor $234650$
CM no
Rank $1$
Graph

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

Elliptic curves in class 234650n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
234650.n2 234650n1 \([1, 0, 1, -293501, -60863352]\) \(3803721481/26000\) \(19112389156250000\) \([2]\) \(4105728\) \(1.9581\) \(\Gamma_0(N)\)-optimal
234650.n3 234650n2 \([1, 0, 1, -113001, -134868352]\) \(-217081801/10562500\) \(-7764408094726562500\) \([2]\) \(8211456\) \(2.3047\)  
234650.n1 234650n3 \([1, 0, 1, -1872876, 946777898]\) \(988345570681/44994560\) \(33075136178240000000\) \([2]\) \(12317184\) \(2.5074\)  
234650.n4 234650n4 \([1, 0, 1, 1015124, 3603737898]\) \(157376536199/7722894400\) \(-5677037045593225000000\) \([2]\) \(24634368\) \(2.8540\)  

Rank

sage: E.rank()
 

The elliptic curves in class 234650n have rank \(1\).

Complex multiplication

The elliptic curves in class 234650n do not have complex multiplication.

Modular form 234650.2.a.n

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.