Properties

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

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Show commands: SageMath
E = EllipticCurve("dh1")
 
E.isogeny_class()
 

Elliptic curves in class 20800.dh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20800.dh1 20800dq2 \([0, 1, 0, -5333, 147713]\) \(671088640/2197\) \(54925000000\) \([]\) \(25920\) \(0.92617\)  
20800.dh2 20800dq1 \([0, 1, 0, -333, -2287]\) \(163840/13\) \(325000000\) \([]\) \(8640\) \(0.37687\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 20800.2.a.dh

sage: E.q_eigenform(10)
 
\(q + q^{3} + 4 q^{7} - 2 q^{9} - 6 q^{11} - q^{13} + 6 q^{17} - 4 q^{19} + O(q^{20})\) 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.