# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("bg1")

sage: E.isogeny_class()

## Elliptic curves in class 5520.bg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5520.bg1 5520be2 $$[0, 1, 0, -50752920, 137408357268]$$ $$3529773792266261468365081/50841342773437500000$$ $$208246140000000000000000$$ $$$$ $$829440$$ $$3.2785$$
5520.bg2 5520be1 $$[0, 1, 0, -364440, 5813802900]$$ $$-1306902141891515161/3564268498800000000$$ $$-14599243771084800000000$$ $$$$ $$414720$$ $$2.9319$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form5520.2.a.bg

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} + 2 q^{7} + q^{9} - 2 q^{11} - 2 q^{13} + q^{15} - 8 q^{19} + O(q^{20})$$

## 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. 