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Properties

Label 9126.u
Number of curves $3$
Conductor $9126$
CM no
Rank $1$
Graph

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

Elliptic curves in class 9126.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9126.u1 9126bj3 \([1, -1, 1, -20819, -1527821]\) \(-1167051/512\) \(-437788023768576\) \([]\) \(38880\) \(1.5166\)  
9126.u2 9126bj1 \([1, -1, 1, -539, 5009]\) \(-132651/2\) \(-260647686\) \([]\) \(4320\) \(0.41796\) \(\Gamma_0(N)\)-optimal
9126.u3 9126bj2 \([1, -1, 1, 1996, 23599]\) \(9261/8\) \(-760048652376\) \([]\) \(12960\) \(0.96727\)  

Rank

sage: E.rank()
 

The elliptic curves in class 9126.u have rank \(1\).

Complex multiplication

The elliptic curves in class 9126.u do not have complex multiplication.

Modular form 9126.2.a.u

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

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.