# Properties

 Label 20160.bb Number of curves $3$ Conductor $20160$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 20160.bb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20160.bb1 20160du3 $$[0, 0, 0, -4728, -130898]$$ $$-250523582464/13671875$$ $$-637875000000$$ $$[]$$ $$25920$$ $$1.0233$$
20160.bb2 20160du1 $$[0, 0, 0, -48, 142]$$ $$-262144/35$$ $$-1632960$$ $$[]$$ $$2880$$ $$-0.075270$$ $$\Gamma_0(N)$$-optimal
20160.bb3 20160du2 $$[0, 0, 0, 312, -362]$$ $$71991296/42875$$ $$-2000376000$$ $$[]$$ $$8640$$ $$0.47404$$

## Rank

sage: E.rank()

The elliptic curves in class 20160.bb have rank $$1$$.

## Complex multiplication

The elliptic curves in class 20160.bb do not have complex multiplication.

## Modular form 20160.2.a.bb

sage: E.q_eigenform(10)

$$q - q^{5} - q^{7} + 3q^{11} - 5q^{13} - 3q^{17} + 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.