Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 10080.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10080.e1 10080m2 \([0, 0, 0, -10083, -389702]\) \(303735479048/105\) \(39191040\) \([2]\) \(12288\) \(0.81289\)  
10080.e2 10080m3 \([0, 0, 0, -1308, 9088]\) \(82881856/36015\) \(107540213760\) \([2]\) \(12288\) \(0.81289\)  
10080.e3 10080m1 \([0, 0, 0, -633, -6032]\) \(601211584/11025\) \(514382400\) \([2, 2]\) \(6144\) \(0.46632\) \(\Gamma_0(N)\)-optimal
10080.e4 10080m4 \([0, 0, 0, -3, -17498]\) \(-8/354375\) \(-132269760000\) \([2]\) \(12288\) \(0.81289\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 10080.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{5} - q^{7} - 4q^{11} + 6q^{13} + 6q^{17} + 4q^{19} + O(q^{20})\)  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.