# Properties

 Label 1680.f Number of curves $4$ Conductor $1680$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 1680.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1680.f1 1680n3 [0, -1, 0, -1800, 30000] [4] 1024
1680.f2 1680n2 [0, -1, 0, -120, 432] [2, 2] 512
1680.f3 1680n1 [0, -1, 0, -40, -80] [2] 256 $$\Gamma_0(N)$$-optimal
1680.f4 1680n4 [0, -1, 0, 280, 2352] [2] 1024

## Rank

sage: E.rank()

The elliptic curves in class 1680.f have rank $$1$$.

## Complex multiplication

The elliptic curves in class 1680.f do not have complex multiplication.

## Modular form1680.2.a.f

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} - q^{7} + q^{9} - 6q^{13} - q^{15} + 2q^{17} + 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.