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Properties

Label 235950hy
Number of curves $2$
Conductor $235950$
CM no
Rank $1$
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Show commands: SageMath
E = EllipticCurve("hy1")
 
E.isogeny_class()
 

Elliptic curves in class 235950hy

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235950.hy2 235950hy1 \([1, 0, 0, 4062, -163008]\) \(356400829/760500\) \(-15816023437500\) \([2]\) \(497664\) \(1.2169\) \(\Gamma_0(N)\)-optimal
235950.hy1 235950hy2 \([1, 0, 0, -31688, -1771758]\) \(169204136291/32906250\) \(684347167968750\) \([2]\) \(995328\) \(1.5635\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 235950.2.a.hy

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