Properties

Label 493680.x
Number of curves $2$
Conductor $493680$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 493680.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
493680.x1 493680x1 \([0, -1, 0, -766, 14995]\) \(-1755904/2295\) \(-65051719920\) \([]\) \(388800\) \(0.76783\) \(\Gamma_0(N)\)-optimal
493680.x2 493680x2 \([0, -1, 0, 6494, -285569]\) \(1068359936/1842375\) \(-52222075158000\) \([]\) \(1166400\) \(1.3171\)  

Rank

sage: E.rank()
 

The elliptic curves in class 493680.x have rank \(0\).

Complex multiplication

The elliptic curves in class 493680.x do not have complex multiplication.

Modular form 493680.2.a.x

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - q^{7} + q^{9} + 4 q^{13} + q^{15} + q^{17} - 7 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.