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Properties

Label 151725cw
Number of curves $2$
Conductor $151725$
CM no
Rank $0$
Graph

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

Elliptic curves in class 151725cw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
151725.cl2 151725cw1 \([1, 1, 0, 324975, -40743000]\) \(2048383/1575\) \(-2918373523168359375\) \([2]\) \(2506752\) \(2.2312\) \(\Gamma_0(N)\)-optimal
151725.cl1 151725cw2 \([1, 1, 0, -1517400, -352104375]\) \(208527857/91875\) \(170238455518154296875\) \([2]\) \(5013504\) \(2.5778\)  

Rank

sage: E.rank()
 

The elliptic curves in class 151725cw have rank \(0\).

Complex multiplication

The elliptic curves in class 151725cw do not have complex multiplication.

Modular form 151725.2.a.cw

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} - q^{4} - q^{6} + q^{7} - 3 q^{8} + q^{9} + 2 q^{11} + q^{12} - 2 q^{13} + q^{14} - q^{16} + q^{18} - 2 q^{19} + O(q^{20})\) 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.