# Properties

 Label 2850.ba Number of curves $2$ Conductor $2850$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("ba1")

sage: E.isogeny_class()

## Elliptic curves in class 2850.ba

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2850.ba1 2850y2 $$[1, 0, 0, -9938, 379992]$$ $$6947097508441/10687500$$ $$166992187500$$ $$$$ $$4608$$ $$1.0528$$
2850.ba2 2850y1 $$[1, 0, 0, -438, 9492]$$ $$-594823321/2166000$$ $$-33843750000$$ $$$$ $$2304$$ $$0.70621$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form2850.2.a.ba

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{6} + 2 q^{7} + q^{8} + q^{9} - 2 q^{11} + q^{12} + 2 q^{14} + q^{16} + 2 q^{17} + q^{18} + q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 