Properties

Label 20800.dx
Number of curves $2$
Conductor $20800$
CM no
Rank $1$
Graph

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

Elliptic curves in class 20800.dx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20800.dx1 20800df2 \([0, -1, 0, -725153, 237921857]\) \(-6434774386429585/140608\) \(-921488588800\) \([]\) \(207360\) \(1.8221\)  
20800.dx2 20800df1 \([0, -1, 0, -8353, 374337]\) \(-9836106385/3407872\) \(-22333829939200\) \([]\) \(69120\) \(1.2728\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 20800.dx have rank \(1\).

Complex multiplication

The elliptic curves in class 20800.dx do not have complex multiplication.

Modular form 20800.2.a.dx

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} + 5 q^{7} + q^{9} - 3 q^{11} + q^{13} - 3 q^{17} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.