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Properties

Label 130130x
Number of curves $2$
Conductor $130130$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 130130x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
130130.x2 130130x1 \([1, -1, 0, -370564, 2338599420]\) \(-1165880220753249/488766923344700\) \(-2359184584502508062300\) \([2]\) \(5806080\) \(2.7802\) \(\Gamma_0(N)\)-optimal
130130.x1 130130x2 \([1, -1, 0, -28774394, 58822455758]\) \(545861123494712462529/6289889684828750\) \(30360096139738573958750\) \([2]\) \(11612160\) \(3.1268\)  

Rank

sage: E.rank()
 

The elliptic curves in class 130130x have rank \(1\).

Complex multiplication

The elliptic curves in class 130130x do not have complex multiplication.

Modular form 130130.2.a.x

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} + q^{7} - q^{8} - 3 q^{9} - q^{10} - q^{11} - q^{14} + q^{16} + 4 q^{17} + 3 q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.