Properties

Label 97461.j
Number of curves $2$
Conductor $97461$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 97461.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
97461.j1 97461b1 [1, -1, 1, -20642852, 36100109350] [2] 6635520 \(\Gamma_0(N)\)-optimal
97461.j2 97461b2 [1, -1, 1, -18731117, 43055001280] [2] 13271040  

Rank

sage: E.rank()
 

The elliptic curves in class 97461.j have rank \(1\).

Complex multiplication

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

Modular form 97461.2.a.j

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 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.