# Properties

 Label 5850.bi Number of curves $2$ Conductor $5850$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 5850.bi

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5850.bi1 5850br2 $$[1, -1, 1, -10355, 365897]$$ $$10779215329/1232010$$ $$14033363906250$$ $$[2]$$ $$18432$$ $$1.2550$$
5850.bi2 5850br1 $$[1, -1, 1, 895, 28397]$$ $$6967871/35100$$ $$-399810937500$$ $$[2]$$ $$9216$$ $$0.90841$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 5850.bi have rank $$0$$.

## Complex multiplication

The elliptic curves in class 5850.bi do not have complex multiplication.

## Modular form5850.2.a.bi

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.