Properties

Label 8016f
Number of curves $2$
Conductor $8016$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8016f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8016.f2 8016f1 \([0, -1, 0, -72, 1008]\) \(-10218313/96192\) \(-394002432\) \([2]\) \(3456\) \(0.33172\) \(\Gamma_0(N)\)-optimal
8016.f1 8016f2 \([0, -1, 0, -1992, 34800]\) \(213525509833/669336\) \(2741600256\) \([2]\) \(6912\) \(0.67830\)  

Rank

sage: E.rank()
 

The elliptic curves in class 8016f have rank \(0\).

Complex multiplication

The elliptic curves in class 8016f do not have complex multiplication.

Modular form 8016.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{3} + 2q^{5} + 4q^{7} + q^{9} + 4q^{11} - 2q^{15} - 4q^{17} + 4q^{19} + O(q^{20})\)  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.