Properties

Label 149058.p
Number of curves $3$
Conductor $149058$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 149058.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
149058.p1 149058er3 \([1, -1, 0, -1941966441, -32939069067059]\) \(-1956469094246217097/36641439744\) \(-15168701749244244227260416\) \([]\) \(125411328\) \(3.9562\)  
149058.p2 149058er2 \([1, -1, 0, -9056826, -100460689484]\) \(-198461344537/10417365504\) \(-4312546435048768150381056\) \([]\) \(41803776\) \(3.4069\)  
149058.p3 149058er1 \([1, -1, 0, 1004589, 3685017181]\) \(270840023/14329224\) \(-5931964646386592768136\) \([]\) \(13934592\) \(2.8576\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 149058.p have rank \(1\).

Complex multiplication

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

Modular form 149058.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 3 q^{5} - q^{8} + 3 q^{10} + 3 q^{11} + q^{16} - 3 q^{17} - 7 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.