# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("2850.m1")

sage: E.isogeny_class()

## Elliptic curves in class 2850.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2850.m1 2850i3 [1, 0, 1, -15526, -744802]  6144
2850.m2 2850i2 [1, 0, 1, -1276, -3802] [2, 2] 3072
2850.m3 2850i1 [1, 0, 1, -776, 8198]  1536 $$\Gamma_0(N)$$-optimal
2850.m4 2850i4 [1, 0, 1, 4974, -28802]  6144

## Rank

sage: E.rank()

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

## 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. 