# Properties

 Label 2850.m Number of curves $4$ Conductor $2850$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("m1")

sage: E.isogeny_class()

## Elliptic curves in class 2850.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2850.m1 2850i3 $$[1, 0, 1, -15526, -744802]$$ $$26487576322129/44531250$$ $$695800781250$$ $$$$ $$6144$$ $$1.1676$$
2850.m2 2850i2 $$[1, 0, 1, -1276, -3802]$$ $$14688124849/8122500$$ $$126914062500$$ $$[2, 2]$$ $$3072$$ $$0.82106$$
2850.m3 2850i1 $$[1, 0, 1, -776, 8198]$$ $$3301293169/22800$$ $$356250000$$ $$$$ $$1536$$ $$0.47449$$ $$\Gamma_0(N)$$-optimal
2850.m4 2850i4 $$[1, 0, 1, 4974, -28802]$$ $$871257511151/527800050$$ $$-8246875781250$$ $$$$ $$6144$$ $$1.1676$$

## Rank

sage: E.rank()

The elliptic curves in class 2850.m have rank $$0$$.

## Complex multiplication

The elliptic curves in class 2850.m do not have complex multiplication.

## Modular form2850.2.a.m

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} + 4q^{11} + q^{12} - 2q^{13} + q^{16} - 2q^{17} - q^{18} - q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 