# Properties

 Label 1600.l Number of curves $2$ Conductor $1600$ CM $$\Q(\sqrt{-1})$$ Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 1600.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality CM discriminant
1600.l1 1600u2 $$[0, 0, 0, -500, 0]$$ $$1728$$ $$8000000000$$ $$[2]$$ $$640$$ $$0.58969$$   $$-4$$
1600.l2 1600u1 $$[0, 0, 0, 125, 0]$$ $$1728$$ $$-125000000$$ $$[2]$$ $$320$$ $$0.24312$$ $$\Gamma_0(N)$$-optimal $$-4$$

## Rank

sage: E.rank()

The elliptic curves in class 1600.l have rank $$1$$.

## Complex multiplication

Each elliptic curve in class 1600.l has complex multiplication by an order in the imaginary quadratic field $$\Q(\sqrt{-1})$$.

## Modular form1600.2.a.l

sage: E.q_eigenform(10)

$$q - 3q^{9} - 4q^{13} + 8q^{17} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.