# Properties

 Label 5520.s Number of curves $2$ Conductor $5520$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("s1")

sage: E.isogeny_class()

## Elliptic curves in class 5520.s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5520.s1 5520f2 $$[0, 1, 0, -856, -9100]$$ $$33909572018/3234375$$ $$6624000000$$ $$$$ $$5376$$ $$0.62231$$
5520.s2 5520f1 $$[0, 1, 0, 64, -636]$$ $$27871484/198375$$ $$-203136000$$ $$$$ $$2688$$ $$0.27573$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form5520.2.a.s

sage: E.q_eigenform(10)

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

## 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. 