Properties

Label 2200.b
Number of curves $2$
Conductor $2200$
CM no
Rank $1$
Graph

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

Elliptic curves in class 2200.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2200.b1 2200d2 \([0, 1, 0, -2208, -32912]\) \(595508/121\) \(242000000000\) \([2]\) \(3200\) \(0.90003\)  
2200.b2 2200d1 \([0, 1, 0, 292, -2912]\) \(5488/11\) \(-5500000000\) \([2]\) \(1600\) \(0.55346\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2200.b have rank \(1\).

Complex multiplication

The elliptic curves in class 2200.b do not have complex multiplication.

Modular form 2200.2.a.b

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