Properties

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

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 11200i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11200.cv2 11200i1 \([0, -1, 0, -33, -4063]\) \(-4/7\) \(-7168000000\) \([2]\) \(5120\) \(0.57005\) \(\Gamma_0(N)\)-optimal
11200.cv1 11200i2 \([0, -1, 0, -4033, -96063]\) \(3543122/49\) \(100352000000\) \([2]\) \(10240\) \(0.91662\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 11200.2.a.i

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