Properties

Label 8976.r
Number of curves $2$
Conductor $8976$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8976.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
8976.r1 8976v2 [0, -1, 0, -2912, -59520] [2] 4608  
8976.r2 8976v1 [0, -1, 0, -192, -768] [2] 2304 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 8976.r have rank \(0\).

Complex multiplication

The elliptic curves in class 8976.r do not have complex multiplication.

Modular form 8976.2.a.r

sage: E.q_eigenform(10)
 
\( q - q^{3} + 2q^{5} + 2q^{7} + q^{9} + q^{11} + 4q^{13} - 2q^{15} + q^{17} - 2q^{19} + O(q^{20}) \)

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.