Properties

Label 200c
Number of curves 4
Conductor 200
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("200.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 200c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
200.c3 200c1 [0, 0, 0, -50, 125] [4] 24 \(\Gamma_0(N)\)-optimal
200.c2 200c2 [0, 0, 0, -175, -750] [2, 2] 48  
200.c1 200c3 [0, 0, 0, -2675, -53250] [2] 96  
200.c4 200c4 [0, 0, 0, 325, -4250] [2] 96  

Rank

sage: E.rank()
 

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

Modular form 200.2.a.c

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.