# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("r1")

sage: E.isogeny_class()

## Elliptic curves in class 5520.r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5520.r1 5520z2 $$[0, 1, 0, -12056, 221844]$$ $$47316161414809/22001657400$$ $$90118788710400$$ $$$$ $$16128$$ $$1.3722$$
5520.r2 5520z1 $$[0, 1, 0, 2664, 27540]$$ $$510273943271/370215360$$ $$-1516402114560$$ $$$$ $$8064$$ $$1.0256$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form5520.2.a.r

sage: E.q_eigenform(10)

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

## 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. 