# Properties

 Label 7200.bb Number of curves $2$ Conductor $7200$ CM $$\Q(\sqrt{-1})$$ Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 7200.bb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality CM discriminant
7200.bb1 7200br1 $$[0, 0, 0, -1125, 0]$$ $$1728$$ $$91125000000$$ $$[2]$$ $$5120$$ $$0.79243$$ $$\Gamma_0(N)$$-optimal $$-4$$
7200.bb2 7200br2 $$[0, 0, 0, 4500, 0]$$ $$1728$$ $$-5832000000000$$ $$[2]$$ $$10240$$ $$1.1390$$   $$-4$$

## Rank

sage: E.rank()

The elliptic curves in class 7200.bb have rank $$0$$.

## Complex multiplication

Each elliptic curve in class 7200.bb has complex multiplication by an order in the imaginary quadratic field $$\Q(\sqrt{-1})$$.

## Modular form7200.2.a.bb

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.