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Properties

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

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 130130.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
130130.t1 130130t2 \([1, -1, 0, -18355, 952251]\) \(311293556218917/3558882250\) \(7818864303250\) \([2]\) \(317952\) \(1.2871\)  
130130.t2 130130t1 \([1, -1, 0, -2105, -12999]\) \(469640998917/235812500\) \(518080062500\) \([2]\) \(158976\) \(0.94050\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 130130.2.a.t

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