# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1680.t1")

sage: E.isogeny_class()

## Elliptic curves in class 1680j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1680.t4 1680j1 [0, 1, 0, -175, -952] [2] 256 $$\Gamma_0(N)$$-optimal
1680.t3 1680j2 [0, 1, 0, -180, -900] [2, 2] 512
1680.t2 1680j3 [0, 1, 0, -680, 5700] [2, 4] 1024
1680.t5 1680j4 [0, 1, 0, 240, -4092] [2] 1024
1680.t1 1680j5 [0, 1, 0, -10480, 409460] [4] 2048
1680.t6 1680j6 [0, 1, 0, 1120, 32340] [4] 2048

## Rank

sage: E.rank()

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

## Modular form1680.2.a.t

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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.