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Properties

Label 166419.t
Number of curves $2$
Conductor $166419$
CM no
Rank $1$
Graph

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

Elliptic curves in class 166419.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
166419.t1 166419t2 \([1, -1, 0, -252465, -48493882]\) \(19034163/121\) \(11313052514847963\) \([2]\) \(1597440\) \(1.9174\)  
166419.t2 166419t1 \([1, -1, 0, -25530, 297143]\) \(19683/11\) \(1028459319531633\) \([2]\) \(798720\) \(1.5708\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 166419.t have rank \(1\).

Complex multiplication

The elliptic curves in class 166419.t do not have complex multiplication.

Modular form 166419.2.a.t

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} + 4 q^{5} + 2 q^{7} - 3 q^{8} + 4 q^{10} - q^{11} + 2 q^{13} + 2 q^{14} - q^{16} + 2 q^{17} + 6 q^{19} + O(q^{20})\) 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.