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Properties

Label 218010.u
Number of curves $2$
Conductor $218010$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 218010.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
218010.u1 218010ch2 \([1, 1, 0, -28016147, -57088532691]\) \(503835593418244309249/898614000000\) \(4337438142726000000\) \([2]\) \(21772800\) \(2.8345\)  
218010.u2 218010ch1 \([1, 1, 0, -1733267, -911504979]\) \(-119305480789133569/5200091136000\) \(-25099846696065024000\) \([2]\) \(10886400\) \(2.4879\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 218010.u have rank \(0\).

Complex multiplication

The elliptic curves in class 218010.u do not have complex multiplication.

Modular form 218010.2.a.u

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} + 4 q^{7} - q^{8} + q^{9} - q^{10} + 4 q^{11} - q^{12} - 4 q^{14} - q^{15} + q^{16} + 4 q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) 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.