# Properties

 Label 5850.bj Number of curves $2$ Conductor $5850$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bj1")

sage: E.isogeny_class()

## Elliptic curves in class 5850.bj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5850.bj1 5850cb2 $$[1, -1, 1, -1445, 3957]$$ $$3659383421/2056392$$ $$187388721000$$ $$$$ $$6144$$ $$0.85317$$
5850.bj2 5850cb1 $$[1, -1, 1, 355, 357]$$ $$54439939/32448$$ $$-2956824000$$ $$$$ $$3072$$ $$0.50660$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 5850.bj have rank $$1$$.

## Complex multiplication

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

## Modular form5850.2.a.bj

sage: E.q_eigenform(10)

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