Properties

Label 2233b
Number of curves $2$
Conductor $2233$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2233b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2233.b1 2233b1 \([0, 1, 1, -63, 271]\) \(-28094464000/20657483\) \(-20657483\) \([3]\) \(336\) \(0.10307\) \(\Gamma_0(N)\)-optimal
2233.b2 2233b2 \([0, 1, 1, 517, -4340]\) \(15252992000000/17621717267\) \(-17621717267\) \([]\) \(1008\) \(0.65238\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2233b have rank \(1\).

Complex multiplication

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

Modular form 2233.2.a.b

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2q^{4} + q^{7} - 2q^{9} - q^{11} - 2q^{12} + 2q^{13} + 4q^{16} + 6q^{17} - 7q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.