Properties

Label 2200.j
Number of curves $2$
Conductor $2200$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 2200.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2200.j1 2200k2 \([0, -1, 0, -88, -228]\) \(595508/121\) \(15488000\) \([2]\) \(640\) \(0.095312\)  
2200.j2 2200k1 \([0, -1, 0, 12, -28]\) \(5488/11\) \(-352000\) \([2]\) \(320\) \(-0.25126\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2200.j have rank \(0\).

Complex multiplication

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

Modular form 2200.2.a.j

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.