Properties

Label 149058.dy
Number of curves $2$
Conductor $149058$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("dy1")
 
E.isogeny_class()
 

Elliptic curves in class 149058.dy

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
149058.dy1 149058in2 \([1, -1, 0, -141738, 20576492]\) \(-67645179/8\) \(-37242383966424\) \([]\) \(995328\) \(1.6296\)  
149058.dy2 149058in1 \([1, -1, 0, 222, 86932]\) \(189/512\) \(-3269564573184\) \([]\) \(331776\) \(1.0803\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 149058.dy have rank \(0\).

Complex multiplication

The elliptic curves in class 149058.dy do not have complex multiplication.

Modular form 149058.2.a.dy

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 3 q^{5} - q^{8} - 3 q^{10} + 3 q^{11} + q^{16} - 6 q^{17} + 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.