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Properties

Label 106134u
Number of curves $2$
Conductor $106134$
CM no
Rank $1$
Graph

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

Elliptic curves in class 106134u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
106134.be2 106134u1 \([1, 0, 1, -18058, -2155366]\) \(-2401/6\) \(-1627260851008086\) \([]\) \(508032\) \(1.6067\) \(\Gamma_0(N)\)-optimal
106134.be1 106134u2 \([1, 0, 1, -2494518, 1573120840]\) \(-6329617441/279936\) \(-75921482264633260416\) \([]\) \(3556224\) \(2.5797\)  

Rank

sage: E.rank()
 

The elliptic curves in class 106134u have rank \(1\).

Complex multiplication

The elliptic curves in class 106134u do not have complex multiplication.

Modular form 106134.2.a.u

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

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.