Properties

Label 22800dk
Number of curves $4$
Conductor $22800$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("22800.dt1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 22800dk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22800.dt4 22800dk1 [0, 1, 0, -4008, -168012] [2] 55296 \(\Gamma_0(N)\)-optimal
22800.dt3 22800dk2 [0, 1, 0, -76008, -8088012] [2, 2] 110592  
22800.dt2 22800dk3 [0, 1, 0, -88008, -5376012] [2] 221184  
22800.dt1 22800dk4 [0, 1, 0, -1216008, -516528012] [2] 221184  

Rank

sage: E.rank()
 

The elliptic curves in class 22800dk have rank \(0\).

Modular form 22800.2.a.dt

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.