# Properties

 Label 5550.bd Number of curves $4$ Conductor $5550$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("bd1")

sage: E.isogeny_class()

## Elliptic curves in class 5550.bd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5550.bd1 5550x4 $$[1, 1, 1, -262188, -23175219]$$ $$127568139540190201/59114336463360$$ $$923661507240000000$$ $$[2]$$ $$145152$$ $$2.1419$$
5550.bd2 5550x2 $$[1, 1, 1, -132813, 18573531]$$ $$16581570075765001/998001000$$ $$15593765625000$$ $$[2]$$ $$48384$$ $$1.5926$$
5550.bd3 5550x1 $$[1, 1, 1, -7813, 323531]$$ $$-3375675045001/999000000$$ $$-15609375000000$$ $$[2]$$ $$24192$$ $$1.2460$$ $$\Gamma_0(N)$$-optimal
5550.bd4 5550x3 $$[1, 1, 1, 57812, -2695219]$$ $$1367594037332999/995878502400$$ $$-15560601600000000$$ $$[2]$$ $$72576$$ $$1.7953$$

## Rank

sage: E.rank()

The elliptic curves in class 5550.bd have rank $$0$$.

## Complex multiplication

The elliptic curves in class 5550.bd do not have complex multiplication.

## Modular form5550.2.a.bd

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} - q^{6} + 4q^{7} + q^{8} + q^{9} + 6q^{11} - q^{12} - 2q^{13} + 4q^{14} + q^{16} + 6q^{17} + q^{18} + 2q^{19} + O(q^{20})$$

## 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.