Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("bb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4032.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4032.bb1 4032g3 \([0, 0, 0, -10764, -429840]\) \(1443468546/7\) \(668860416\) \([2]\) \(4096\) \(0.89385\)  
4032.bb2 4032g4 \([0, 0, 0, -2124, 29808]\) \(11090466/2401\) \(229419122688\) \([2]\) \(4096\) \(0.89385\)  
4032.bb3 4032g2 \([0, 0, 0, -684, -6480]\) \(740772/49\) \(2341011456\) \([2, 2]\) \(2048\) \(0.54727\)  
4032.bb4 4032g1 \([0, 0, 0, 36, -432]\) \(432/7\) \(-83607552\) \([2]\) \(1024\) \(0.20070\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4032.2.a.bb

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