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Properties

Label 8280a
Number of curves $2$
Conductor $8280$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 8280a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8280.k1 8280a1 \([0, 0, 0, -18, 17]\) \(1492992/575\) \(248400\) \([2]\) \(896\) \(-0.26571\) \(\Gamma_0(N)\)-optimal
8280.k2 8280a2 \([0, 0, 0, 57, 122]\) \(2963088/2645\) \(-18282240\) \([2]\) \(1792\) \(0.080860\)  

Rank

sage: E.rank()
 

The elliptic curves in class 8280a have rank \(1\).

Complex multiplication

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

Modular form 8280.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{5} + 2 q^{7} - 4 q^{11} + 2 q^{13} + 2 q^{17} - 8 q^{19} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.