Properties

Label 22800cp
Number of curves $2$
Conductor $22800$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cp1")
 
E.isogeny_class()
 

Elliptic curves in class 22800cp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22800.z2 22800cp1 \([0, -1, 0, 2632, -33168]\) \(3936827539/3158028\) \(-1616910336000\) \([2]\) \(32256\) \(1.0305\) \(\Gamma_0(N)\)-optimal
22800.z1 22800cp2 \([0, -1, 0, -12568, -276368]\) \(428831641421/181752822\) \(93057444864000\) \([2]\) \(64512\) \(1.3771\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 22800.2.a.cp

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.