# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("z1")

sage: E.isogeny_class()

## Elliptic curves in class 5520.z

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5520.z1 5520y2 $$[0, 1, 0, -1856, -30156]$$ $$172715635009/7935000$$ $$32501760000$$ $$$$ $$4608$$ $$0.77868$$
5520.z2 5520y1 $$[0, 1, 0, 64, -1740]$$ $$6967871/331200$$ $$-1356595200$$ $$$$ $$2304$$ $$0.43211$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form5520.2.a.z

sage: E.q_eigenform(10)

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