Properties

Label 22800cy
Number of curves $4$
Conductor $22800$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cy1")
 
E.isogeny_class()
 

Elliptic curves in class 22800cy

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22800.df3 22800cy1 \([0, 1, 0, -10348408, -12934304812]\) \(-1914980734749238129/20440940544000\) \(-1308220194816000000000\) \([2]\) \(1658880\) \(2.8683\) \(\Gamma_0(N)\)-optimal
22800.df2 22800cy2 \([0, 1, 0, -165996408, -823237792812]\) \(7903870428425797297009/886464000000\) \(56733696000000000000\) \([2]\) \(3317760\) \(3.2149\)  
22800.df4 22800cy3 \([0, 1, 0, 34195592, -67299488812]\) \(69096190760262356111/70568821500000000\) \(-4516404576000000000000000\) \([2]\) \(4976640\) \(3.4177\)  
22800.df1 22800cy4 \([0, 1, 0, -185292408, -619970272812]\) \(10993009831928446009969/3767761230468750000\) \(241136718750000000000000000\) \([2]\) \(9953280\) \(3.7642\)  

Rank

sage: E.rank()
 

The elliptic curves in class 22800cy have rank \(1\).

Complex multiplication

The elliptic curves in class 22800cy do not have complex multiplication.

Modular form 22800.2.a.cy

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.