# Properties

 Label 1008j Number of curves 4 Conductor 1008 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1008.g1")

sage: E.isogeny_class()

## Elliptic curves in class 1008j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1008.g4 1008j1 [0, 0, 0, 60, -61]  192 $$\Gamma_0(N)$$-optimal
1008.g3 1008j2 [0, 0, 0, -255, -502]  384
1008.g2 1008j3 [0, 0, 0, -1020, -12913]  576
1008.g1 1008j4 [0, 0, 0, -16455, -812446]  1152

## Rank

sage: E.rank()

The elliptic curves in class 1008j have rank $$1$$.

## Modular form1008.2.a.g

sage: E.q_eigenform(10)

$$q - q^{7} - 6q^{11} + 2q^{13} + 4q^{19} + O(q^{20})$$

## 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. 