Properties

Label 5040.bm
Number of curves $4$
Conductor $5040$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bm1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5040.bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5040.bm1 5040bn3 \([0, 0, 0, -38547, -2912814]\) \(2121328796049/120050\) \(358467379200\) \([2]\) \(12288\) \(1.2814\)  
5040.bm2 5040bn4 \([0, 0, 0, -12627, 510354]\) \(74565301329/5468750\) \(16329600000000\) \([2]\) \(12288\) \(1.2814\)  
5040.bm3 5040bn2 \([0, 0, 0, -2547, -40014]\) \(611960049/122500\) \(365783040000\) \([2, 2]\) \(6144\) \(0.93487\)  
5040.bm4 5040bn1 \([0, 0, 0, 333, -3726]\) \(1367631/2800\) \(-8360755200\) \([2]\) \(3072\) \(0.58829\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5040.bm have rank \(1\).

Complex multiplication

The elliptic curves in class 5040.bm do not have complex multiplication.

Modular form 5040.2.a.bm

sage: E.q_eigenform(10)
 
\(q + q^{5} + q^{7} + 4q^{11} - 6q^{13} - 2q^{17} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.