Properties

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

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

Elliptic curves in class 97461.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
97461.j1 97461b1 \([1, -1, 1, -20642852, 36100109350]\) \(420100556152674123/62939003491\) \(145746923103770267097\) \([2]\) \(6635520\) \(2.8823\) \(\Gamma_0(N)\)-optimal
97461.j2 97461b2 \([1, -1, 1, -18731117, 43055001280]\) \(-313859434290315003/164114213839849\) \(-380036867094225826804683\) \([2]\) \(13271040\) \(3.2289\)  

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)
 
\(q - q^{2} - q^{4} - 4 q^{5} + 3 q^{8} + 4 q^{10} + q^{13} - q^{16} - q^{17} + 4 q^{19} + O(q^{20})\) Copy content 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.