# Properties

 Label 1600g Number of curves 4 Conductor 1600 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1600.c1")

sage: E.isogeny_class()

## Elliptic curves in class 1600g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1600.c3 1600g1 [0, 1, 0, -133, 363]  384 $$\Gamma_0(N)$$-optimal
1600.c4 1600g2 [0, 1, 0, 367, 2863]  768
1600.c1 1600g3 [0, 1, 0, -4133, -103637]  1152
1600.c2 1600g4 [0, 1, 0, -3633, -129137]  2304

## Rank

sage: E.rank()

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

## Modular form1600.2.a.c

sage: E.q_eigenform(10)

$$q - 2q^{3} - 2q^{7} + q^{9} + 2q^{13} + 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 