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Properties

Label 130130d
Number of curves $2$
Conductor $130130$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 130130d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
130130.d2 130130d1 \([1, 0, 1, -5285479, 2695786602]\) \(1539878581036333/594987008000\) \(6309539353279145984000\) \([2]\) \(15095808\) \(2.8820\) \(\Gamma_0(N)\)-optimal
130130.d1 130130d2 \([1, 0, 1, -74183399, 245850325866]\) \(4257490797851938093/1434818000000\) \(15215526581369114000000\) \([2]\) \(30191616\) \(3.2286\)  

Rank

sage: E.rank()
 

The elliptic curves in class 130130d have rank \(0\).

Complex multiplication

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

Modular form 130130.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} - 2 q^{3} + q^{4} - q^{5} + 2 q^{6} - q^{7} - q^{8} + q^{9} + q^{10} - q^{11} - 2 q^{12} + q^{14} + 2 q^{15} + q^{16} - 6 q^{17} - q^{18} + 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.