Properties

Label 2233.a
Number of curves $4$
Conductor $2233$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2233.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2233.a1 2233a4 \([1, -1, 1, -53356, 4756540]\) \(16798320881842096017/2132227789307\) \(2132227789307\) \([2]\) \(5376\) \(1.3875\)  
2233.a2 2233a3 \([1, -1, 1, -21166, -1131504]\) \(1048626554636928177/48569076788309\) \(48569076788309\) \([2]\) \(5376\) \(1.3875\)  
2233.a3 2233a2 \([1, -1, 1, -3621, 61556]\) \(5249244962308257/1448621666569\) \(1448621666569\) \([2, 2]\) \(2688\) \(1.0409\)  
2233.a4 2233a1 \([1, -1, 1, 584, 6050]\) \(22062729659823/29354283343\) \(-29354283343\) \([4]\) \(1344\) \(0.69438\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2233.a have rank \(0\).

Complex multiplication

The elliptic curves in class 2233.a do not have complex multiplication.

Modular form 2233.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} - 2q^{5} - q^{7} + 3q^{8} - 3q^{9} + 2q^{10} - q^{11} + 6q^{13} + q^{14} - q^{16} - 2q^{17} + 3q^{18} - 8q^{19} + O(q^{20})\)  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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.