Properties

Label 200.d
Number of curves $2$
Conductor $200$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 200.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
200.d1 200d2 \([0, -1, 0, -708, 7412]\) \(78608\) \(500000000\) \([2]\) \(80\) \(0.47807\)  
200.d2 200d1 \([0, -1, 0, -83, -88]\) \(2048\) \(31250000\) \([2]\) \(40\) \(0.13150\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 200.d have rank \(0\).

Complex multiplication

The elliptic curves in class 200.d do not have complex multiplication.

Modular form 200.2.a.d

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.