Properties

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

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 2200.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2200.c1 2200j2 \([0, 1, 0, -5708, -104912]\) \(41141648/14641\) \(7320500000000\) \([2]\) \(3840\) \(1.1695\)  
2200.c2 2200j1 \([0, 1, 0, -5083, -141162]\) \(464857088/121\) \(3781250000\) \([2]\) \(1920\) \(0.82291\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2200.2.a.c

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