# Properties

 Label 2800.bd Number of curves $2$ Conductor $2800$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("bd1")

sage: E.isogeny_class()

## Elliptic curves in class 2800.bd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2800.bd1 2800g2 $$[0, -1, 0, -1008, 12512]$$ $$3543122/49$$ $$1568000000$$ $$[2]$$ $$1280$$ $$0.57005$$
2800.bd2 2800g1 $$[0, -1, 0, -8, 512]$$ $$-4/7$$ $$-112000000$$ $$[2]$$ $$640$$ $$0.22348$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 2800.bd have rank $$0$$.

## Complex multiplication

The elliptic curves in class 2800.bd do not have complex multiplication.

## Modular form2800.2.a.bd

sage: E.q_eigenform(10)

$$q + 2q^{3} + q^{7} + q^{9} + 2q^{17} + 2q^{19} + O(q^{20})$$

## 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.