# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("i1")

sage: E.isogeny_class()

## Elliptic curves in class 1200i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1200.l2 1200i1 $$[0, 1, 0, 32, 68]$$ $$27436/27$$ $$-3456000$$ $$$$ $$192$$ $$-0.058373$$ $$\Gamma_0(N)$$-optimal
1200.l1 1200i2 $$[0, 1, 0, -168, 468]$$ $$2060602/729$$ $$186624000$$ $$$$ $$384$$ $$0.28820$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1200.2.a.i

sage: E.q_eigenform(10)

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