# Properties

 Label 4410.bb Number of curves $2$ Conductor $4410$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 4410.bb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4410.bb1 4410w2 $$[1, -1, 1, -16148, -785753]$$ $$68971442301/400$$ $$2700507600$$ $$[2]$$ $$6144$$ $$0.99993$$
4410.bb2 4410w1 $$[1, -1, 1, -1028, -11609]$$ $$17779581/1280$$ $$8641624320$$ $$[2]$$ $$3072$$ $$0.65336$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 4410.bb have rank $$1$$.

## Complex multiplication

The elliptic curves in class 4410.bb do not have complex multiplication.

## Modular form4410.2.a.bb

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{5} + q^{8} - q^{10} + 2q^{11} - 2q^{13} + q^{16} - 2q^{17} - 6q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.