Properties

Label 10080.bf
Number of curves $4$
Conductor $10080$
CM no
Rank $0$
Graph

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

Elliptic curves in class 10080.bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10080.bf1 10080by2 \([0, 0, 0, -2916147, -1916735686]\) \(7347751505995469192/72930375\) \(27221116608000\) \([2]\) \(122880\) \(2.1542\)  
10080.bf2 10080by3 \([0, 0, 0, -261147, -1567186]\) \(5276930158229192/3050936350875\) \(1138755891091392000\) \([2]\) \(122880\) \(2.1542\)  
10080.bf3 10080by1 \([0, 0, 0, -182397, -29901436]\) \(14383655824793536/45209390625\) \(2109289329000000\) \([2, 2]\) \(61440\) \(1.8076\) \(\Gamma_0(N)\)-optimal
10080.bf4 10080by4 \([0, 0, 0, -105852, -55191904]\) \(-43927191786304/415283203125\) \(-1240029000000000000\) \([4]\) \(122880\) \(2.1542\)  

Rank

sage: E.rank()
 

The elliptic curves in class 10080.bf have rank \(0\).

Complex multiplication

The elliptic curves in class 10080.bf do not have complex multiplication.

Modular form 10080.2.a.bf

sage: E.q_eigenform(10)
 
\(q + q^{5} - q^{7} - 4 q^{11} - 2 q^{13} + 2 q^{17} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.