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Properties

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

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Show commands: SageMath
E = EllipticCurve("cq1")
 
E.isogeny_class()
 

Elliptic curves in class 151725.cq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
151725.cq1 151725cn2 \([1, 0, 1, -102329235751, -11701251565603477]\) \(63953244990201015504593/5088175635498046875\) \(9428061622773232373394012451171875\) \([2]\) \(827228160\) \(5.2626\)  
151725.cq2 151725cn1 \([1, 0, 1, 6461165624, -825475140144727]\) \(16098893047132187167/168182866341984375\) \(-311632015354292206693808349609375\) \([2]\) \(413614080\) \(4.9160\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 151725.2.a.cq

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 LMFDB 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 LMFDB labels.