Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 97461c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
97461.x1 97461c1 [1, -1, 0, -2293650, -1336276537] [2] 2211840 \(\Gamma_0(N)\)-optimal
97461.x2 97461c2 [1, -1, 0, -2081235, -1593935932] [2] 4423680  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 97461.2.a.c

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

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 Cremona 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 Cremona labels.