# Properties

 Label 55440.db Number of curves $4$ Conductor $55440$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("db1")

sage: E.isogeny_class()

## Elliptic curves in class 55440.db

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
55440.db1 55440dy4 $$[0, 0, 0, -446367, 60520826]$$ $$52702650535889104/22020583921875$$ $$4109569453836000000$$ $$[2]$$ $$995328$$ $$2.2687$$
55440.db2 55440dy2 $$[0, 0, 0, -384807, 91878194]$$ $$33766427105425744/9823275$$ $$1833258873600$$ $$[2]$$ $$331776$$ $$1.7194$$
55440.db3 55440dy1 $$[0, 0, 0, -23952, 1447931]$$ $$-130287139815424/2250652635$$ $$-26251612334640$$ $$[2]$$ $$165888$$ $$1.3728$$ $$\Gamma_0(N)$$-optimal
55440.db4 55440dy3 $$[0, 0, 0, 92688, 6938759]$$ $$7549996227362816/6152409907875$$ $$-71761709165454000$$ $$[2]$$ $$497664$$ $$1.9222$$

## Rank

sage: E.rank()

The elliptic curves in class 55440.db have rank $$0$$.

## Complex multiplication

The elliptic curves in class 55440.db do not have complex multiplication.

## Modular form 55440.2.a.db

sage: E.q_eigenform(10)

$$q + q^{5} - q^{7} - q^{11} + 2q^{13} + 6q^{17} - 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.