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Properties

Label 149058.ca
Number of curves $2$
Conductor $149058$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("ca1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

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

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(3\)\(1\)
\(7\)\(1\)
\(13\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(5\) \( 1 + 5 T^{2}\) 1.5.a
\(11\) \( 1 + 3 T + 11 T^{2}\) 1.11.d
\(17\) \( 1 - 3 T + 17 T^{2}\) 1.17.ad
\(19\) \( 1 + 5 T + 19 T^{2}\) 1.19.f
\(23\) \( 1 + 6 T + 23 T^{2}\) 1.23.g
\(29\) \( 1 - 3 T + 29 T^{2}\) 1.29.ad
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

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

Modular form 149058.2.a.ca

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

Isogeny matrix

Copy content 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

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 149058.ca

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
149058.ca1 149058fp2 \([1, -1, 0, -2274687, -1319903285]\) \(531373116625/2058\) \(5041207202311098\) \([]\) \(2322432\) \(2.2264\)  
149058.ca2 149058fp1 \([1, -1, 0, -38817, -292811]\) \(2640625/1512\) \(3703744067004072\) \([]\) \(774144\) \(1.6770\) \(\Gamma_0(N)\)-optimal