# Properties

 Label 200400m 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 200400m

sage: E.isogeny_class().curves

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

## Rank

sage: E.rank()

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

## Modular form 200400.2.a.bs

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 Cremona 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 Cremona labels. 