Properties

Label 465690.o
Number of curves $2$
Conductor $465690$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 465690.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
465690.o1 465690o2 [1, 0, 1, -59845144, 178188084326] [2] 69672960 \(\Gamma_0(N)\)-optimal*
465690.o2 465690o1 [1, 0, 1, -3702424, 2843141222] [2] 34836480 \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 465690.o1.

Rank

sage: E.rank()
 

The elliptic curves in class 465690.o have rank \(1\).

Complex multiplication

The elliptic curves in class 465690.o do not have complex multiplication.

Modular form 465690.2.a.o

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - 4q^{7} - q^{8} + q^{9} + q^{10} - 4q^{11} + q^{12} - 4q^{13} + 4q^{14} - q^{15} + q^{16} + 4q^{17} - q^{18} + O(q^{20}) \)

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.