Properties

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

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 2730.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2730.g1 2730g1 \([1, 1, 0, -8127, 273861]\) \(59374229431741561/1153923563520\) \(1153923563520\) \([2]\) \(6720\) \(1.1071\) \(\Gamma_0(N)\)-optimal
2730.g2 2730g2 \([1, 1, 0, 193, 817989]\) \(788632918919/288997521321600\) \(-288997521321600\) \([2]\) \(13440\) \(1.4537\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2730.2.a.g

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