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Properties

Label 4998.x
Number of curves $2$
Conductor $4998$
CM no
Rank $0$
Graph

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

Elliptic curves in class 4998.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4998.x1 4998x1 \([1, 0, 1, -124, -346]\) \(1771561/612\) \(72001188\) \([2]\) \(2880\) \(0.20943\) \(\Gamma_0(N)\)-optimal
4998.x2 4998x2 \([1, 0, 1, 366, -2306]\) \(46268279/46818\) \(-5508090882\) \([2]\) \(5760\) \(0.55600\)  

Rank

sage: E.rank()
 

The elliptic curves in class 4998.x have rank \(0\).

Complex multiplication

The elliptic curves in class 4998.x do not have complex multiplication.

Modular form 4998.2.a.x

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.