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Properties

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

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 9200v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9200.h2 9200v1 \([0, 1, 0, -2708, -53912]\) \(878800/23\) \(57500000000\) \([]\) \(10080\) \(0.84612\) \(\Gamma_0(N)\)-optimal
9200.h1 9200v2 \([0, 1, 0, -27708, 1746088]\) \(941054800/12167\) \(30417500000000\) \([]\) \(30240\) \(1.3954\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 9200.2.a.v

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} - q^{7} + q^{9} + 3 q^{11} - 5 q^{13} - 6 q^{17} + 7 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.