Properties

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

Related objects

Downloads

Learn more about

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

Elliptic curves in class 200.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
200.c1 200c3 \([0, 0, 0, -2675, -53250]\) \(132304644/5\) \(80000000\) \([2]\) \(96\) \(0.60250\)  
200.c2 200c2 \([0, 0, 0, -175, -750]\) \(148176/25\) \(100000000\) \([2, 2]\) \(48\) \(0.25593\)  
200.c3 200c1 \([0, 0, 0, -50, 125]\) \(55296/5\) \(1250000\) \([4]\) \(24\) \(-0.090642\) \(\Gamma_0(N)\)-optimal
200.c4 200c4 \([0, 0, 0, 325, -4250]\) \(237276/625\) \(-10000000000\) \([2]\) \(96\) \(0.60250\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 200.2.a.c

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.