Properties

Label 169050.t
Number of curves $2$
Conductor $169050$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 169050.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
169050.t1 169050ih1 \([1, 1, 0, -1320820750, -18476804343500]\) \(138626767243242683688529/5300196249600\) \(9743168571393600000000\) \([2]\) \(53084160\) \(3.7105\) \(\Gamma_0(N)\)-optimal
169050.t2 169050ih2 \([1, 1, 0, -1318860750, -18534371503500]\) \(-138010547060620856386129/857302254769101120\) \(-1575949265177030901045000000\) \([2]\) \(106168320\) \(4.0571\)  

Rank

sage: E.rank()
 

The elliptic curves in class 169050.t have rank \(0\).

Complex multiplication

The elliptic curves in class 169050.t do not have complex multiplication.

Modular form 169050.2.a.t

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.