Properties

Label 235950.x
Number of curves $2$
Conductor $235950$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 235950.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235950.x1 235950x2 \([1, 1, 0, -84547905, 298927703925]\) \(301832602552272335237/309456388859904\) \(68527608713130048768000\) \([2]\) \(36495360\) \(3.3000\)  
235950.x2 235950x1 \([1, 1, 0, -4010305, 6978903925]\) \(-32209943913443717/76420466343936\) \(-16922939722091200512000\) \([2]\) \(18247680\) \(2.9535\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 235950.x have rank \(1\).

Complex multiplication

The elliptic curves in class 235950.x do not have complex multiplication.

Modular form 235950.2.a.x

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