Properties

Label 11200.cg
Number of curves $3$
Conductor $11200$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("cg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11200.cg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11200.cg1 11200c3 \([0, 1, 0, -13133, -610387]\) \(-250523582464/13671875\) \(-13671875000000\) \([]\) \(20736\) \(1.2788\)  
11200.cg2 11200c1 \([0, 1, 0, -133, 613]\) \(-262144/35\) \(-35000000\) \([]\) \(2304\) \(0.18014\) \(\Gamma_0(N)\)-optimal
11200.cg3 11200c2 \([0, 1, 0, 867, -1387]\) \(71991296/42875\) \(-42875000000\) \([]\) \(6912\) \(0.72945\)  

Rank

sage: E.rank()
 

The elliptic curves in class 11200.cg have rank \(1\).

Complex multiplication

The elliptic curves in class 11200.cg do not have complex multiplication.

Modular form 11200.2.a.cg

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{7} - 2q^{9} + 3q^{11} + 5q^{13} - 3q^{17} - 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.