# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("1200.l1")

sage: E.isogeny_class()

## Elliptic curves in class 1200.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1200.l1 1200i2 [0, 1, 0, -168, 468]  384
1200.l2 1200i1 [0, 1, 0, 32, 68]  192 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form1200.2.a.l

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 LMFDB 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 LMFDB labels. 