# Properties

 Label 1200n Number of curves $2$ Conductor $1200$ CM no Rank $1$ Graph

# Learn more

Show commands for: SageMath
sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

## Elliptic curves in class 1200n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1200.a1 1200n1 $$[0, -1, 0, -333, -2088]$$ $$131072/9$$ $$281250000$$ $$[2]$$ $$480$$ $$0.36947$$ $$\Gamma_0(N)$$-optimal
1200.a2 1200n2 $$[0, -1, 0, 292, -9588]$$ $$5488/81$$ $$-40500000000$$ $$[2]$$ $$960$$ $$0.71604$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1200.2.a.n

sage: E.q_eigenform(10)

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

## 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 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.