Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("x1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 97461.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
97461.x1 97461c1 \([1, -1, 0, -2293650, -1336276537]\) \(420100556152674123/62939003491\) \(199927192186241793\) \([2]\) \(2211840\) \(2.3330\) \(\Gamma_0(N)\)-optimal
97461.x2 97461c2 \([1, -1, 0, -2081235, -1593935932]\) \(-313859434290315003/164114213839849\) \(-521312574889198665027\) \([2]\) \(4423680\) \(2.6796\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 97461.2.a.x

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} + 4q^{5} - 3q^{8} + 4q^{10} + q^{13} - q^{16} + q^{17} + 4q^{19} + O(q^{20})\)  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 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.