Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8280.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8280.h1 8280b2 \([0, 0, 0, -243, -658]\) \(28697814/13225\) \(731289600\) \([2]\) \(2560\) \(0.39559\)  
8280.h2 8280b1 \([0, 0, 0, -123, 518]\) \(7443468/115\) \(3179520\) \([2]\) \(1280\) \(0.049019\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 8280.2.a.h

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