# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

## Elliptic curves in class 5520.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5520.l1 5520t2 $$[0, -1, 0, -62800, 6078400]$$ $$6687281588245201/165600$$ $$678297600$$ $$$$ $$11520$$ $$1.2131$$
5520.l2 5520t1 $$[0, -1, 0, -3920, 96192]$$ $$-1626794704081/8125440$$ $$-33281802240$$ $$$$ $$5760$$ $$0.86648$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form5520.2.a.l

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} + q^{9} + 2q^{11} + 4q^{13} - q^{15} + 6q^{17} + 8q^{19} + O(q^{20})$$ ## 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. 