# Properties

 Label 5850.e Number of curves $2$ Conductor $5850$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("e1")

E.isogeny_class()

## Elliptic curves in class 5850.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5850.e1 5850ba2 $$[1, -1, 0, -31707, -2158299]$$ $$38686490446661/141927552$$ $$12933148176000$$ $$$$ $$28672$$ $$1.3763$$
5850.e2 5850ba1 $$[1, -1, 0, -2907, 1701]$$ $$29819839301/17252352$$ $$1572120576000$$ $$$$ $$14336$$ $$1.0298$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form5850.2.a.e

sage: E.q_eigenform(10)

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

## 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. 