# Properties

 Label 200.c Number of curves 4 Conductor 200 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("200.c1")

sage: E.isogeny_class()

## Elliptic curves in class 200.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
200.c1 200c3 [0, 0, 0, -2675, -53250]  96
200.c2 200c2 [0, 0, 0, -175, -750] [2, 2] 48
200.c3 200c1 [0, 0, 0, -50, 125]  24 $$\Gamma_0(N)$$-optimal
200.c4 200c4 [0, 0, 0, 325, -4250]  96

## Rank

sage: E.rank()

The elliptic curves in class 200.c have rank $$0$$.

## Modular form200.2.a.c

sage: E.q_eigenform(10)

$$q + 4q^{7} - 3q^{9} + 4q^{11} + 2q^{13} - 2q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 