Properties

Label 5200.v
Number of curves $2$
Conductor $5200$
CM no
Rank $0$
Graph

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

Elliptic curves in class 5200.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5200.v1 5200q2 \([0, 1, 0, -853, 9283]\) \(671088640/2197\) \(224972800\) \([]\) \(2592\) \(0.46803\)  
5200.v2 5200q1 \([0, 1, 0, -53, -157]\) \(163840/13\) \(1331200\) \([]\) \(864\) \(-0.081277\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5200.v have rank \(0\).

Complex multiplication

The elliptic curves in class 5200.v do not have complex multiplication.

Modular form 5200.2.a.v

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