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Properties

Label 2730.j
Number of curves $2$
Conductor $2730$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 2730.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2730.j1 2730j1 \([1, 1, 0, -142, -524]\) \(320153881321/91990080\) \(91990080\) \([2]\) \(960\) \(0.23453\) \(\Gamma_0(N)\)-optimal
2730.j2 2730j2 \([1, 1, 0, 378, -2916]\) \(5948434379159/7522842600\) \(-7522842600\) \([2]\) \(1920\) \(0.58110\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2730.j have rank \(0\).

Complex multiplication

The elliptic curves in class 2730.j do not have complex multiplication.

Modular form 2730.2.a.j

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