Properties

Label 20800.dy
Number of curves $2$
Conductor $20800$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("dy1")
 
E.isogeny_class()
 

Elliptic curves in class 20800.dy

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20800.dy1 20800bn2 \([0, -1, 0, -18128833, -29703974463]\) \(-6434774386429585/140608\) \(-14398259200000000\) \([]\) \(1036800\) \(2.6268\)  
20800.dy2 20800bn1 \([0, -1, 0, -208833, -46374463]\) \(-9836106385/3407872\) \(-348966092800000000\) \([]\) \(345600\) \(2.0775\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 20800.dy have rank \(0\).

Complex multiplication

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

Modular form 20800.2.a.dy

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.