# Properties

 Label 1680.q Number of curves $6$ Conductor $1680$ CM no Rank $0$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("1680.q1")

sage: E.isogeny_class()

## Elliptic curves in class 1680.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1680.q1 1680t5 [0, 1, 0, -268800, 53550900] [4] 6144
1680.q2 1680t4 [0, 1, 0, -16800, 832500] [2, 4] 3072
1680.q3 1680t6 [0, 1, 0, -15680, 949428] [8] 6144
1680.q4 1680t3 [0, 1, 0, -5920, -167692] [2] 3072
1680.q5 1680t2 [0, 1, 0, -1120, 10868] [2, 2] 1536
1680.q6 1680t1 [0, 1, 0, 160, 1140] [2] 768 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form1680.2.a.q

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} - q^{7} + q^{9} - 4q^{11} - 2q^{13} + q^{15} + 2q^{17} + 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.