# Properties

 Label 1200.r Number of curves $4$ Conductor $1200$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("r1")

sage: E.isogeny_class()

## Elliptic curves in class 1200.r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1200.r1 1200g4 $$[0, 1, 0, -5408, 151188]$$ $$546718898/405$$ $$12960000000$$ $$$$ $$1536$$ $$0.87412$$
1200.r2 1200g3 $$[0, 1, 0, -3408, -76812]$$ $$136835858/1875$$ $$60000000000$$ $$$$ $$1536$$ $$0.87412$$
1200.r3 1200g2 $$[0, 1, 0, -408, 1188]$$ $$470596/225$$ $$3600000000$$ $$[2, 2]$$ $$768$$ $$0.52755$$
1200.r4 1200g1 $$[0, 1, 0, 92, 188]$$ $$21296/15$$ $$-60000000$$ $$$$ $$384$$ $$0.18097$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1200.2.a.r

sage: E.q_eigenform(10)

$$q + q^{3} + 4q^{7} + q^{9} + 6q^{13} + 2q^{17} - 4q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 