# Properties

 Label 3850.o Number of curves $2$ Conductor $3850$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("o1")

sage: E.isogeny_class()

## Elliptic curves in class 3850.o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3850.o1 3850v2 $$[1, 0, 0, -5863, -173283]$$ $$1426487591593/2156$$ $$33687500$$ $$$$ $$4096$$ $$0.71240$$
3850.o2 3850v1 $$[1, 0, 0, -363, -2783]$$ $$-338608873/13552$$ $$-211750000$$ $$$$ $$2048$$ $$0.36583$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3850.o have rank $$0$$.

## Complex multiplication

The elliptic curves in class 3850.o do not have complex multiplication.

## Modular form3850.2.a.o

sage: E.q_eigenform(10)

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

## 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. 