# Properties

 Label 1200.a Number of curves $2$ Conductor $1200$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 1200.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1200.a1 1200n1 $$[0, -1, 0, -333, -2088]$$ $$131072/9$$ $$281250000$$ $$$$ $$480$$ $$0.36947$$ $$\Gamma_0(N)$$-optimal
1200.a2 1200n2 $$[0, -1, 0, 292, -9588]$$ $$5488/81$$ $$-40500000000$$ $$$$ $$960$$ $$0.71604$$

## Rank

sage: E.rank()

The elliptic curves in class 1200.a have rank $$1$$.

## Complex multiplication

The elliptic curves in class 1200.a do not have complex multiplication.

## Modular form1200.2.a.a

sage: E.q_eigenform(10)

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

## 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. 