Properties

Label 8280.v
Number of curves $4$
Conductor $8280$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("v1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8280.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8280.v1 8280v3 \([0, 0, 0, -22107, -1265146]\) \(1600610497636/9315\) \(6953610240\) \([2]\) \(14336\) \(1.0786\)  
8280.v2 8280v2 \([0, 0, 0, -1407, -19006]\) \(1650587344/119025\) \(22212921600\) \([2, 2]\) \(7168\) \(0.73198\)  
8280.v3 8280v1 \([0, 0, 0, -282, 1469]\) \(212629504/43125\) \(503010000\) \([4]\) \(3584\) \(0.38541\) \(\Gamma_0(N)\)-optimal
8280.v4 8280v4 \([0, 0, 0, 1293, -83266]\) \(320251964/4197615\) \(-3133502807040\) \([2]\) \(14336\) \(1.0786\)  

Rank

sage: E.rank()
 

The elliptic curves in class 8280.v have rank \(0\).

Complex multiplication

The elliptic curves in class 8280.v do not have complex multiplication.

Modular form 8280.2.a.v

sage: E.q_eigenform(10)
 
\(q + q^{5} + 4 q^{7} - 4 q^{11} + 6 q^{13} + 2 q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.