# Properties

 Label 200.c Number of curves $4$ Conductor $200$ CM no Rank $0$ Graph # Learn more about

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

sage: E.isogeny_class()

## Elliptic curves in class 200.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
200.c1 200c3 $$[0, 0, 0, -2675, -53250]$$ $$132304644/5$$ $$80000000$$ $$$$ $$96$$ $$0.60250$$
200.c2 200c2 $$[0, 0, 0, -175, -750]$$ $$148176/25$$ $$100000000$$ $$[2, 2]$$ $$48$$ $$0.25593$$
200.c3 200c1 $$[0, 0, 0, -50, 125]$$ $$55296/5$$ $$1250000$$ $$$$ $$24$$ $$-0.090642$$ $$\Gamma_0(N)$$-optimal
200.c4 200c4 $$[0, 0, 0, 325, -4250]$$ $$237276/625$$ $$-10000000000$$ $$$$ $$96$$ $$0.60250$$

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 200.c do not have complex multiplication.

## 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. 