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Properties

Label 25350cw
Number of curves $2$
Conductor $25350$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cw1")
 
E.isogeny_class()
 

Elliptic curves in class 25350cw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25350.dh2 25350cw1 \([1, 0, 0, 16812, -2327508]\) \(6967871/35100\) \(-2647203060937500\) \([2]\) \(193536\) \(1.6416\) \(\Gamma_0(N)\)-optimal
25350.dh1 25350cw2 \([1, 0, 0, -194438, -29578758]\) \(10779215329/1232010\) \(92916827438906250\) \([2]\) \(387072\) \(1.9881\)  

Rank

sage: E.rank()
 

The elliptic curves in class 25350cw have rank \(1\).

Complex multiplication

The elliptic curves in class 25350cw do not have complex multiplication.

Modular form 25350.2.a.cw

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + 2 q^{7} + q^{8} + q^{9} - 4 q^{11} + q^{12} + 2 q^{14} + q^{16} - 8 q^{17} + q^{18} + 6 q^{19} + O(q^{20})\) 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.