Properties

Label 4560.ba
Number of curves $4$
Conductor $4560$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("ba1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4560.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.ba1 4560j3 \([0, 1, 0, -2440, -47212]\) \(784767874322/35625\) \(72960000\) \([2]\) \(3072\) \(0.58494\)  
4560.ba2 4560j4 \([0, 1, 0, -760, 7220]\) \(23735908082/1954815\) \(4003461120\) \([2]\) \(3072\) \(0.58494\)  
4560.ba3 4560j2 \([0, 1, 0, -160, -700]\) \(445138564/81225\) \(83174400\) \([2, 2]\) \(1536\) \(0.23837\)  
4560.ba4 4560j1 \([0, 1, 0, 20, -52]\) \(3286064/7695\) \(-1969920\) \([2]\) \(768\) \(-0.10820\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4560.ba have rank \(0\).

Complex multiplication

The elliptic curves in class 4560.ba do not have complex multiplication.

Modular form 4560.2.a.ba

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.