Properties

Label 6720.bu
Number of curves $2$
Conductor $6720$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("bu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6720.bu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6720.bu1 6720by2 \([0, 1, 0, -841, -8041]\) \(16079333824/2953125\) \(12096000000\) \([2]\) \(4608\) \(0.65316\)  
6720.bu2 6720by1 \([0, 1, 0, 104, -670]\) \(1925134784/4465125\) \(-285768000\) \([2]\) \(2304\) \(0.30659\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 6720.bu have rank \(0\).

Complex multiplication

The elliptic curves in class 6720.bu do not have complex multiplication.

Modular form 6720.2.a.bu

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + q^{7} + q^{9} + 2 q^{11} + 4 q^{13} - q^{15} - 2 q^{17} - 6 q^{19} + O(q^{20})\) 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.