Properties

Label 149058bw
Number of curves $2$
Conductor $149058$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("bw1")
 
E.isogeny_class()
 

Elliptic curves in class 149058bw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
149058.hg2 149058bw1 \([1, -1, 1, 53212153, -1688104631937]\) \(40251338884511/2997011332224\) \(-1240692815435975560139435136\) \([]\) \(75866112\) \(3.8783\) \(\Gamma_0(N)\)-optimal
149058.hg1 149058bw2 \([1, -1, 1, -273856513937, -55161007239852237]\) \(-5486773802537974663600129/2635437714\) \(-1091009767674920875345746\) \([]\) \(531062784\) \(4.8513\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 149058.2.a.bw

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

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.