Properties

Label 4032bj
Number of curves $4$
Conductor $4032$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bj1")
 
E.isogeny_class()
 

Elliptic curves in class 4032bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4032.bk4 4032bj1 \([0, 0, 0, 36, 432]\) \(432/7\) \(-83607552\) \([2]\) \(1024\) \(0.20070\) \(\Gamma_0(N)\)-optimal
4032.bk3 4032bj2 \([0, 0, 0, -684, 6480]\) \(740772/49\) \(2341011456\) \([2, 2]\) \(2048\) \(0.54727\)  
4032.bk2 4032bj3 \([0, 0, 0, -2124, -29808]\) \(11090466/2401\) \(229419122688\) \([2]\) \(4096\) \(0.89385\)  
4032.bk1 4032bj4 \([0, 0, 0, -10764, 429840]\) \(1443468546/7\) \(668860416\) \([2]\) \(4096\) \(0.89385\)  

Rank

sage: E.rank()
 

The elliptic curves in class 4032bj have rank \(0\).

Complex multiplication

The elliptic curves in class 4032bj do not have complex multiplication.

Modular form 4032.2.a.bj

sage: E.q_eigenform(10)
 
\(q + 2 q^{5} + q^{7} + 4 q^{11} - 2 q^{13} + 6 q^{17} + 8 q^{19} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.