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Properties

Label 9200e
Number of curves $2$
Conductor $9200$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 9200e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9200.x2 9200e1 \([0, 0, 0, 125, -750]\) \(13500/23\) \(-368000000\) \([2]\) \(3456\) \(0.32860\) \(\Gamma_0(N)\)-optimal
9200.x1 9200e2 \([0, 0, 0, -875, -7750]\) \(2315250/529\) \(16928000000\) \([2]\) \(6912\) \(0.67517\)  

Rank

sage: E.rank()
 

The elliptic curves in class 9200e have rank \(0\).

Complex multiplication

The elliptic curves in class 9200e do not have complex multiplication.

Modular form 9200.2.a.e

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