Properties

Label 6288d
Number of curves $2$
Conductor $6288$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 6288d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6288.d2 6288d1 \([0, -1, 0, -34160, -2298432]\) \(1076291879750641/60150618144\) \(246376931917824\) \([]\) \(20160\) \(1.5165\) \(\Gamma_0(N)\)-optimal
6288.d1 6288d2 \([0, -1, 0, -3632720, 2666200128]\) \(1294373635812597347281/2083292441154\) \(8533165838966784\) \([]\) \(100800\) \(2.3212\)  

Rank

sage: E.rank()
 

The elliptic curves in class 6288d have rank \(0\).

Complex multiplication

The elliptic curves in class 6288d do not have complex multiplication.

Modular form 6288.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} - 3 q^{7} + q^{9} + 3 q^{11} + 4 q^{13} - q^{15} - 7 q^{17} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.