Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 97461.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
97461.k1 97461i1 \([1, -1, 1, -20075, 1033386]\) \(10431681625/710073\) \(60900206836833\) \([2]\) \(294912\) \(1.3935\) \(\Gamma_0(N)\)-optimal
97461.k2 97461i2 \([1, -1, 1, 17410, 4422030]\) \(6804992375/102626433\) \(-8801871070476393\) \([2]\) \(589824\) \(1.7401\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 97461.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} + 3q^{8} - 4q^{11} - q^{13} - q^{16} - q^{17} + 8q^{19} + O(q^{20})\)  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.