# Properties

 Label 1200.g Number of curves $4$ Conductor $1200$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 1200.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1200.g1 1200m4 $$[0, -1, 0, -13248, -580608]$$ $$502270291349/1889568$$ $$967458816000$$ $$$$ $$1920$$ $$1.1592$$
1200.g2 1200m2 $$[0, -1, 0, -848, 9792]$$ $$131872229/18$$ $$9216000$$ $$$$ $$384$$ $$0.35445$$
1200.g3 1200m3 $$[0, -1, 0, -448, -17408]$$ $$-19465109/248832$$ $$-127401984000$$ $$$$ $$960$$ $$0.81260$$
1200.g4 1200m1 $$[0, -1, 0, -48, 192]$$ $$-24389/12$$ $$-6144000$$ $$$$ $$192$$ $$0.0078760$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1200.2.a.g

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rrrr} 1 & 5 & 2 & 10 \\ 5 & 1 & 10 & 2 \\ 2 & 10 & 1 & 5 \\ 10 & 2 & 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 