# Properties

 Label 1680.o Number of curves $4$ Conductor $1680$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("o1")

sage: E.isogeny_class()

## Elliptic curves in class 1680.o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1680.o1 1680r3 [0, 1, 0, -5976, -179820]  1536
1680.o2 1680r2 [0, 1, 0, -376, -2860] [2, 2] 768
1680.o3 1680r1 [0, 1, 0, -56, 84]  384 $$\Gamma_0(N)$$-optimal
1680.o4 1680r4 [0, 1, 0, 104, -9196]  1536

## Rank

sage: E.rank()

The elliptic curves in class 1680.o have rank $$0$$.

## Complex multiplication

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

## Modular form1680.2.a.o

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} + q^{7} + q^{9} + 4q^{11} - 2q^{13} - q^{15} - 6q^{17} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 