Properties

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

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Show commands: SageMath
E = EllipticCurve("hm1")
 
E.isogeny_class()
 

Elliptic curves in class 235950hm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235950.hm2 235950hm1 \([1, 0, 0, -5523713, 5063991417]\) \(-673350049820449/10617750000\) \(-293906121996093750000\) \([2]\) \(13271040\) \(2.7289\) \(\Gamma_0(N)\)-optimal
235950.hm1 235950hm2 \([1, 0, 0, -88711213, 321592428917]\) \(2789222297765780449/677605500\) \(18756554331023437500\) \([2]\) \(26542080\) \(3.0754\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 235950.2.a.hm

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.