Properties

Label 97461.p
Number of curves $2$
Conductor $97461$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 97461.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
97461.p1 97461n1 [1, -1, 0, -200664, 34629979] [2] 860160 \(\Gamma_0(N)\)-optimal
97461.p2 97461n2 [1, -1, 0, -163179, 47937154] [2] 1720320  

Rank

sage: E.rank()
 

The elliptic curves in class 97461.p have rank \(0\).

Complex multiplication

The elliptic curves in class 97461.p do not have complex multiplication.

Modular form 97461.2.a.p

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{4} - 4q^{5} - 3q^{8} - 4q^{10} + 4q^{11} - q^{13} - q^{16} + q^{17} + O(q^{20}) \)

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.