# Properties

 Label 5520.y Number of curves $2$ Conductor $5520$ CM no Rank $0$ Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("y1")

sage: E.isogeny_class()

## Elliptic curves in class 5520.y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5520.y1 5520bc2 $$[0, 1, 0, -27976, 1569140]$$ $$591202341974089/79350000000$$ $$325017600000000$$ $$$$ $$21504$$ $$1.5121$$
5520.y2 5520bc1 $$[0, 1, 0, 2744, 131444]$$ $$557644990391/2119680000$$ $$-8682209280000$$ $$$$ $$10752$$ $$1.1655$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 5520.y have rank $$0$$.

## Complex multiplication

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

## Modular form5520.2.a.y

sage: E.q_eigenform(10)

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