# Properties

 Label 5550.ba Number of curves $2$ Conductor $5550$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("ba1")

sage: E.isogeny_class()

## Elliptic curves in class 5550.ba

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5550.ba1 5550v2 $$[1, 1, 1, -177213, -28823469]$$ $$-39390416456458249/56832000000$$ $$-888000000000000$$ $$[]$$ $$51840$$ $$1.7707$$
5550.ba2 5550v1 $$[1, 1, 1, 3162, -185469]$$ $$223759095911/1094104800$$ $$-17095387500000$$ $$[]$$ $$17280$$ $$1.2214$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form5550.2.a.ba

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 