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Properties

Label 11200cr
Number of curves $2$
Conductor $11200$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cr1")
 
E.isogeny_class()
 

Elliptic curves in class 11200cr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11200.p2 11200cr1 \([0, 1, 0, 167, -537]\) \(8000/7\) \(-448000000\) \([2]\) \(4608\) \(0.34752\) \(\Gamma_0(N)\)-optimal
11200.p1 11200cr2 \([0, 1, 0, -833, -5537]\) \(125000/49\) \(25088000000\) \([2]\) \(9216\) \(0.69409\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 11200.2.a.cr

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