Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8976.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
8976.s1 8976q1 [0, -1, 0, -3136, 68608] [2] 9216 \(\Gamma_0(N)\)-optimal
8976.s2 8976q2 [0, -1, 0, -2496, 96768] [2] 18432  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 8976.2.a.s

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

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.