# Properties

 Label 5520.q Number of curves $4$ Conductor $5520$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("q1")

E.isogeny_class()

## Elliptic curves in class 5520.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5520.q1 5520e3 $$[0, 1, 0, -2456, -47676]$$ $$1600610497636/9315$$ $$9538560$$ $$[2]$$ $$3584$$ $$0.52925$$
5520.q2 5520e2 $$[0, 1, 0, -156, -756]$$ $$1650587344/119025$$ $$30470400$$ $$[2, 2]$$ $$1792$$ $$0.18267$$
5520.q3 5520e1 $$[0, 1, 0, -31, 44]$$ $$212629504/43125$$ $$690000$$ $$[2]$$ $$896$$ $$-0.16390$$ $$\Gamma_0(N)$$-optimal
5520.q4 5520e4 $$[0, 1, 0, 144, -3036]$$ $$320251964/4197615$$ $$-4298357760$$ $$[2]$$ $$3584$$ $$0.52925$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form5520.2.a.q

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} - 4 q^{7} + q^{9} - 4 q^{11} + 6 q^{13} - q^{15} - 2 q^{17} - 4 q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.