# Properties

 Label 1200.o Number of curves $6$ Conductor $1200$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("o1")

sage: E.isogeny_class()

## Elliptic curves in class 1200.o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1200.o1 1200e5 $$[0, 1, 0, -80008, 8683988]$$ $$1770025017602/75$$ $$2400000000$$ $$[2]$$ $$3072$$ $$1.2847$$
1200.o2 1200e3 $$[0, 1, 0, -5008, 133988]$$ $$868327204/5625$$ $$90000000000$$ $$[2, 2]$$ $$1536$$ $$0.93814$$
1200.o3 1200e6 $$[0, 1, 0, -2008, 295988]$$ $$-27995042/1171875$$ $$-37500000000000$$ $$[2]$$ $$3072$$ $$1.2847$$
1200.o4 1200e2 $$[0, 1, 0, -508, -1012]$$ $$3631696/2025$$ $$8100000000$$ $$[2, 2]$$ $$768$$ $$0.59157$$
1200.o5 1200e1 $$[0, 1, 0, -383, -3012]$$ $$24918016/45$$ $$11250000$$ $$[2]$$ $$384$$ $$0.24500$$ $$\Gamma_0(N)$$-optimal
1200.o6 1200e4 $$[0, 1, 0, 1992, -6012]$$ $$54607676/32805$$ $$-524880000000$$ $$[4]$$ $$1536$$ $$0.93814$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1200.2.a.o

sage: E.q_eigenform(10)

$$q + q^{3} + q^{9} + 4 q^{11} - 6 q^{13} + 6 q^{17} + 4 q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.