# Properties

 Label 5520.bb Number of curves $2$ Conductor $5520$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 5520.bb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5520.bb1 5520bg2 $$[0, 1, 0, -3880, 91700]$$ $$1577505447721/838350$$ $$3433881600$$ $$$$ $$6912$$ $$0.77950$$
5520.bb2 5520bg1 $$[0, 1, 0, -200, 1908]$$ $$-217081801/285660$$ $$-1170063360$$ $$$$ $$3456$$ $$0.43292$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 5520.bb have rank $$1$$.

## Complex multiplication

The elliptic curves in class 5520.bb do not have complex multiplication.

## Modular form5520.2.a.bb

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} - 4q^{7} + q^{9} - 2q^{11} + 4q^{13} + q^{15} - 6q^{17} + 4q^{19} + O(q^{20})$$ ## 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. 