Properties

Label 7200.bg
Number of curves $4$
Conductor $7200$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 7200.bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7200.bg1 7200g3 \([0, 0, 0, -18300, 952000]\) \(14526784/15\) \(699840000000\) \([2]\) \(12288\) \(1.1908\)  
7200.bg2 7200g2 \([0, 0, 0, -12675, -544250]\) \(38614472/405\) \(2361960000000\) \([2]\) \(12288\) \(1.1908\)  
7200.bg3 7200g1 \([0, 0, 0, -1425, 7000]\) \(438976/225\) \(164025000000\) \([2, 2]\) \(6144\) \(0.84418\) \(\Gamma_0(N)\)-optimal
7200.bg4 7200g4 \([0, 0, 0, 5325, 54250]\) \(2863288/1875\) \(-10935000000000\) \([2]\) \(12288\) \(1.1908\)  

Rank

sage: E.rank()
 

The elliptic curves in class 7200.bg have rank \(0\).

Complex multiplication

The elliptic curves in class 7200.bg do not have complex multiplication.

Modular form 7200.2.a.bg

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