Properties

Label 20800.bd
Number of curves $3$
Conductor $20800$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bd1")
 
E.isogeny_class()
 

Elliptic curves in class 20800.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20800.bd1 20800db3 \([0, -1, 0, -735233, 242898337]\) \(-10730978619193/6656\) \(-27262976000000\) \([]\) \(124416\) \(1.8988\)  
20800.bd2 20800db2 \([0, -1, 0, -7233, 474337]\) \(-10218313/17576\) \(-71991296000000\) \([]\) \(41472\) \(1.3495\)  
20800.bd3 20800db1 \([0, -1, 0, 767, -13663]\) \(12167/26\) \(-106496000000\) \([]\) \(13824\) \(0.80021\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 20800.2.a.bd

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

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.