Properties

Label 3600.bg
Number of curves $4$
Conductor $3600$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bg1")
 
E.isogeny_class()
 

Elliptic curves in class 3600.bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3600.bg1 3600bm4 \([0, 0, 0, -119235, 15795650]\) \(502270291349/1889568\) \(705277476864000\) \([2]\) \(15360\) \(1.7085\)  
3600.bg2 3600bm2 \([0, 0, 0, -7635, -256750]\) \(131872229/18\) \(6718464000\) \([2]\) \(3072\) \(0.90376\)  
3600.bg3 3600bm3 \([0, 0, 0, -4035, 474050]\) \(-19465109/248832\) \(-92876046336000\) \([2]\) \(7680\) \(1.3619\)  
3600.bg4 3600bm1 \([0, 0, 0, -435, -4750]\) \(-24389/12\) \(-4478976000\) \([2]\) \(1536\) \(0.55718\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3600.bg have rank \(0\).

Complex multiplication

The elliptic curves in class 3600.bg do not have complex multiplication.

Modular form 3600.2.a.bg

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

\(\left(\begin{array}{rrrr} 1 & 5 & 2 & 10 \\ 5 & 1 & 10 & 2 \\ 2 & 10 & 1 & 5 \\ 10 & 2 & 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.