Properties

Label 130.c
Number of curves $2$
Conductor $130$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 130.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
130.c1 130c1 \([1, 1, 1, -841, -9737]\) \(65787589563409/10400000\) \(10400000\) \([2]\) \(80\) \(0.35695\) \(\Gamma_0(N)\)-optimal
130.c2 130c2 \([1, 1, 1, -761, -11561]\) \(-48743122863889/26406250000\) \(-26406250000\) \([2]\) \(160\) \(0.70352\)  

Rank

sage: E.rank()
 

The elliptic curves in class 130.c have rank \(0\).

Complex multiplication

The elliptic curves in class 130.c do not have complex multiplication.

Modular form 130.2.a.c

sage: E.q_eigenform(10)
 
\(q + q^{2} + 2q^{3} + q^{4} - q^{5} + 2q^{6} - 4q^{7} + q^{8} + q^{9} - q^{10} - 2q^{11} + 2q^{12} - q^{13} - 4q^{14} - 2q^{15} + q^{16} + 2q^{17} + q^{18} + 6q^{19} + O(q^{20})\)  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.