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 j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
97461.p1 97461n1 \([1, -1, 0, -200664, 34629979]\) \(10418796526321/6390657\) \(548101861531497\) \([2]\) \(860160\) \(1.7709\) \(\Gamma_0(N)\)-optimal
97461.p2 97461n2 \([1, -1, 0, -163179, 47937154]\) \(-5602762882081/8312741073\) \(-712951556708587833\) \([2]\) \(1720320\) \(2.1175\)  

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