Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("ca1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 22800ca

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22800.t3 22800ca1 \([0, -1, 0, -12408, -524688]\) \(3301293169/22800\) \(1459200000000\) \([2]\) \(36864\) \(1.1676\) \(\Gamma_0(N)\)-optimal
22800.t2 22800ca2 \([0, -1, 0, -20408, 243312]\) \(14688124849/8122500\) \(519840000000000\) \([2, 2]\) \(73728\) \(1.5142\)  
22800.t4 22800ca3 \([0, -1, 0, 79592, 1843312]\) \(871257511151/527800050\) \(-33779203200000000\) \([2]\) \(147456\) \(1.8608\)  
22800.t1 22800ca4 \([0, -1, 0, -248408, 47667312]\) \(26487576322129/44531250\) \(2850000000000000\) \([2]\) \(147456\) \(1.8608\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 22800.2.a.ca

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.