Properties

Label 4800.q
Number of curves $6$
Conductor $4800$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4800.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4800.q1 4800c5 \([0, -1, 0, -38433, -2887263]\) \(3065617154/9\) \(18432000000\) \([2]\) \(8192\) \(1.1991\)  
4800.q2 4800c4 \([0, -1, 0, -6433, 200737]\) \(28756228/3\) \(3072000000\) \([2]\) \(4096\) \(0.85251\)  
4800.q3 4800c3 \([0, -1, 0, -2433, -43263]\) \(1556068/81\) \(82944000000\) \([2, 2]\) \(4096\) \(0.85251\)  
4800.q4 4800c2 \([0, -1, 0, -433, 2737]\) \(35152/9\) \(2304000000\) \([2, 2]\) \(2048\) \(0.50594\)  
4800.q5 4800c1 \([0, -1, 0, 67, 237]\) \(2048/3\) \(-48000000\) \([2]\) \(1024\) \(0.15937\) \(\Gamma_0(N)\)-optimal
4800.q6 4800c6 \([0, -1, 0, 1567, -175263]\) \(207646/6561\) \(-13436928000000\) \([2]\) \(8192\) \(1.1991\)  

Rank

sage: E.rank()
 

The elliptic curves in class 4800.q have rank \(1\).

Complex multiplication

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

Modular form 4800.2.a.q

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

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.