Properties

Label 132600.bb
Number of curves $4$
Conductor $132600$
CM no
Rank $0$
Graph

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

Elliptic curves in class 132600.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
132600.bb1 132600y4 \([0, -1, 0, -2256008, -971537988]\) \(79364416584061444/20404090514925\) \(326465448238800000000\) \([2]\) \(4718592\) \(2.6456\)  
132600.bb2 132600y2 \([0, -1, 0, -793508, 259887012]\) \(13813960087661776/714574355625\) \(2858297422500000000\) \([2, 2]\) \(2359296\) \(2.2990\)  
132600.bb3 132600y1 \([0, -1, 0, -783383, 267136512]\) \(212670222886967296/616241925\) \(154060481250000\) \([2]\) \(1179648\) \(1.9524\) \(\Gamma_0(N)\)-optimal
132600.bb4 132600y3 \([0, -1, 0, 506992, 1027182012]\) \(900753985478876/29018422265625\) \(-464294756250000000000\) \([2]\) \(4718592\) \(2.6456\)  

Rank

sage: E.rank()
 

The elliptic curves in class 132600.bb have rank \(0\).

Complex multiplication

The elliptic curves in class 132600.bb do not have complex multiplication.

Modular form 132600.2.a.bb

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.