Properties

Label 8280.l
Number of curves $2$
Conductor $8280$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8280.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8280.l1 8280e2 \([0, 0, 0, -8643, 254558]\) \(47825527682/8926875\) \(13327752960000\) \([2]\) \(18432\) \(1.2364\)  
8280.l2 8280e1 \([0, 0, 0, 1077, 23222]\) \(185073116/419175\) \(-312912460800\) \([2]\) \(9216\) \(0.88986\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 8280.2.a.l

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.