# Properties

 Label 1200.h Number of curves $2$ Conductor $1200$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("h1")

sage: E.isogeny_class()

## Elliptic curves in class 1200.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1200.h1 1200b2 $$[0, -1, 0, -4208, 66912]$$ $$2060602/729$$ $$2916000000000$$ $$[2]$$ $$1920$$ $$1.0929$$
1200.h2 1200b1 $$[0, -1, 0, 792, 6912]$$ $$27436/27$$ $$-54000000000$$ $$[2]$$ $$960$$ $$0.74635$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1200.h have rank $$0$$.

## Complex multiplication

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

## Modular form1200.2.a.h

sage: E.q_eigenform(10)

$$q - q^{3} + 2 q^{7} + q^{9} - 2 q^{11} + 2 q^{13} + 6 q^{17} - 8 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.