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Properties

Label 272734.bf
Number of curves $2$
Conductor $272734$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bf1")
 
E.isogeny_class()
 

Elliptic curves in class 272734.bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
272734.bf1 272734bf2 \([1, 0, 1, -186777403629, -31069519745555700]\) \(3457421777436801623930814481/2690147821103679244\) \(560687011665666210869308172716\) \([]\) \(1036800000\) \(5.0155\)  
272734.bf2 272734bf1 \([1, 0, 1, -1533743489, 21526037081140]\) \(1914421473306136725841/147437307865222144\) \(30729234619184238881187490816\) \([]\) \(207360000\) \(4.2108\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 272734.bf have rank \(0\).

Complex multiplication

The elliptic curves in class 272734.bf do not have complex multiplication.

Modular form 272734.2.a.bf

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

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.