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Properties

Label 1098.l
Number of curves $2$
Conductor $1098$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 1098.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1098.l1 1098l1 \([1, -1, 1, -41, -547]\) \(-10218313/177876\) \(-129671604\) \([]\) \(384\) \(0.23786\) \(\Gamma_0(N)\)-optimal
1098.l2 1098l2 \([1, -1, 1, 364, 14519]\) \(7335308807/130741056\) \(-95310229824\) \([3]\) \(1152\) \(0.78717\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1098.l have rank \(0\).

Complex multiplication

The elliptic curves in class 1098.l do not have complex multiplication.

Modular form 1098.2.a.l

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + 3 q^{5} - q^{7} + q^{8} + 3 q^{10} + 3 q^{11} - q^{13} - q^{14} + q^{16} + 6 q^{17} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.