Properties

Label 141570dx
Number of curves $2$
Conductor $141570$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("dx1")
 
E.isogeny_class()
 

Elliptic curves in class 141570dx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141570.n2 141570dx1 \([1, -1, 0, -726930, 320519700]\) \(-32894113444921/15289560000\) \(-19745977000103640000\) \([2]\) \(3686400\) \(2.4087\) \(\Gamma_0(N)\)-optimal
141570.n1 141570dx2 \([1, -1, 0, -12705930, 17433719100]\) \(175654575624148921/21954418200\) \(28353427883330635800\) \([2]\) \(7372800\) \(2.7552\)  

Rank

sage: E.rank()
 

The elliptic curves in class 141570dx have rank \(1\).

Complex multiplication

The elliptic curves in class 141570dx do not have complex multiplication.

Modular form 141570.2.a.dx

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} - q^{13} + q^{16} - 4 q^{17} + 2 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.