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Properties

Label 64974.g
Number of curves $2$
Conductor $64974$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 64974.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64974.g1 64974n2 \([1, 1, 0, -64705, 6277279]\) \(742446841375/4188834\) \(169034561024238\) \([2]\) \(365568\) \(1.5721\)  
64974.g2 64974n1 \([1, 1, 0, -6395, -31863]\) \(716917375/405756\) \(16373718161892\) \([2]\) \(182784\) \(1.2255\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 64974.g have rank \(0\).

Complex multiplication

The elliptic curves in class 64974.g do not have complex multiplication.

Modular form 64974.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} - 4 q^{11} - q^{12} + q^{13} + q^{16} + q^{17} - q^{18} + O(q^{20})\) 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.