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Properties

Label 64974i
Number of curves $2$
Conductor $64974$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 64974i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64974.o2 64974i1 \([1, 1, 0, 5054619, -6110248563]\) \(121394948260111009847/207438591806724096\) \(-24404942887469283170304\) \([]\) \(5930496\) \(2.9807\) \(\Gamma_0(N)\)-optimal
64974.o1 64974i2 \([1, 1, 0, -48348276, 232580724048]\) \(-106237652098524394207033/137183418749137453056\) \(-16139492032417272214585344\) \([]\) \(17791488\) \(3.5300\)  

Rank

sage: E.rank()
 

The elliptic curves in class 64974i have rank \(1\).

Complex multiplication

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

Modular form 64974.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + 3 q^{5} + q^{6} - q^{8} + q^{9} - 3 q^{10} - q^{12} - q^{13} - 3 q^{15} + q^{16} + q^{17} - q^{18} - 2 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.