# Properties

 Label 1200.f Number of curves $2$ Conductor $1200$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

## Elliptic curves in class 1200.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1200.f1 1200l2 $$[0, -1, 0, -30333, 2043537]$$ $$-30866268160/3$$ $$-300000000$$ $$[]$$ $$2160$$ $$1.0599$$
1200.f2 1200l1 $$[0, -1, 0, -333, 3537]$$ $$-40960/27$$ $$-2700000000$$ $$[]$$ $$720$$ $$0.51063$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1200.2.a.f

sage: E.q_eigenform(10)

$$q - q^{3} + q^{7} + q^{9} - 6q^{11} + 5q^{13} - 6q^{17} - 5q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 