# Properties

 Label 200400.bs Number of curves 2 Conductor 200400 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("200400.bs1")
sage: E.isogeny_class()

## Elliptic curves in class 200400.bs

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
200400.bs1 200400m2 [0, 1, 0, -49808, 4250388] 2 884736
200400.bs2 200400m1 [0, 1, 0, -1808, 122388] 2 442368 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 200400.bs have rank $$0$$.

## Modular form None

sage: E.q_eigenform(10)
$$q + q^{3} - 4q^{7} + q^{9} + 4q^{11} + 4q^{17} + 4q^{19} + O(q^{20})$$

## 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.