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Properties

Label 106134.t
Number of curves $2$
Conductor $106134$
CM no
Rank $2$
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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 106134.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
106134.t1 106134bk1 \([1, 0, 1, -5955, 298750]\) \(-549754417/592704\) \(-25172902875456\) \([]\) \(311040\) \(1.2663\) \(\Gamma_0(N)\)-optimal
106134.t2 106134bk2 \([1, 0, 1, 49905, -5398970]\) \(323648023823/484243284\) \(-20566436461073076\) \([]\) \(933120\) \(1.8156\)  

Rank

sage: E.rank()
 

The elliptic curves in class 106134.t have rank \(2\).

Complex multiplication

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

Modular form 106134.2.a.t

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - 3 q^{5} - q^{6} - q^{8} + q^{9} + 3 q^{10} - 3 q^{11} + q^{12} + 2 q^{13} - 3 q^{15} + q^{16} - 3 q^{17} - q^{18} + O(q^{20})\) 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 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.