Properties

Label 4800.cp
Number of curves $2$
Conductor $4800$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("cp1")
 
E.isogeny_class()
 

Elliptic curves in class 4800.cp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4800.cp1 4800cr2 \([0, 1, 0, -2153, -39177]\) \(2156689088/81\) \(41472000\) \([2]\) \(3072\) \(0.54809\)  
4800.cp2 4800cr1 \([0, 1, 0, -128, -702]\) \(-29218112/6561\) \(-52488000\) \([2]\) \(1536\) \(0.20152\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4800.cp have rank \(0\).

Complex multiplication

The elliptic curves in class 4800.cp do not have complex multiplication.

Modular form 4800.2.a.cp

sage: E.q_eigenform(10)
 
\(q + q^{3} + 4 q^{7} + q^{9} - 4 q^{13} - 8 q^{19} + O(q^{20})\) 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.