# Properties

 Label 56550.bi Number of curves $2$ Conductor $56550$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("bi1")

sage: E.isogeny_class()

## Elliptic curves in class 56550.bi

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
56550.bi1 56550bk1 $$[1, 1, 1, -20813, 974531]$$ $$63812982460681/10201800960$$ $$159403140000000$$ $$[2]$$ $$184320$$ $$1.4476$$ $$\Gamma_0(N)$$-optimal
56550.bi2 56550bk2 $$[1, 1, 1, 37187, 5498531]$$ $$363979050334199/1041836936400$$ $$-16278702131250000$$ $$[2]$$ $$368640$$ $$1.7942$$

## Rank

sage: E.rank()

The elliptic curves in class 56550.bi have rank $$1$$.

## Complex multiplication

The elliptic curves in class 56550.bi do not have complex multiplication.

## Modular form 56550.2.a.bi

sage: E.q_eigenform(10)

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

## 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.