# Properties

 Label 1008h Number of curves $4$ Conductor $1008$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("h1")

sage: E.isogeny_class()

## Elliptic curves in class 1008h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1008.d4 1008h1 [0, 0, 0, 9, 54] [2] 128 $$\Gamma_0(N)$$-optimal
1008.d3 1008h2 [0, 0, 0, -171, 810] [2, 2] 256
1008.d2 1008h3 [0, 0, 0, -531, -3726] [2] 512
1008.d1 1008h4 [0, 0, 0, -2691, 53730] [2] 512

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 1008h do not have complex multiplication.

## Modular form1008.2.a.h

sage: E.q_eigenform(10)

$$q - 2q^{5} + q^{7} - 4q^{11} + 2q^{13} + 6q^{17} - 8q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels.