# Properties

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

# Related objects

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 form7200.2.a.bg

sage: E.q_eigenform(10)

$$q + 4q^{11} - 2q^{13} - 2q^{17} - 8q^{19} + O(q^{20})$$

## 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.