Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 97461.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
97461.r1 97461a2 \([1, -1, 0, -242853, -17548210]\) \(684030715731/338005577\) \(782714534822734059\) \([2]\) \(1105920\) \(2.1266\)  
97461.r2 97461a1 \([1, -1, 0, -130398, 17965079]\) \(105890949891/1288651\) \(2984110135004817\) \([2]\) \(552960\) \(1.7800\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 97461.2.a.r

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