Properties

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

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 8280.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8280.w1 8280w2 \([0, 0, 0, -7707, -237994]\) \(33909572018/3234375\) \(4828896000000\) \([2]\) \(21504\) \(1.1716\)  
8280.w2 8280w1 \([0, 0, 0, 573, -17746]\) \(27871484/198375\) \(-148086144000\) \([2]\) \(10752\) \(0.82504\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 8280.2.a.w

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