Properties

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

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 235950z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235950.z2 235950z1 \([1, 1, 0, -46950, 3384000]\) \(3307949/468\) \(1619317476562500\) \([2]\) \(1382400\) \(1.6443\) \(\Gamma_0(N)\)-optimal
235950.z1 235950z2 \([1, 1, 0, -198200, -30647250]\) \(248858189/27378\) \(94730072378906250\) \([2]\) \(2764800\) \(1.9909\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 235950.2.a.z

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