# Properties

 Label 1008.i Number of curves $2$ Conductor $1008$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1008.i1")

sage: E.isogeny_class()

## Elliptic curves in class 1008.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1008.i1 1008a1 [0, 0, 0, -54, 135]  192 $$\Gamma_0(N)$$-optimal
1008.i2 1008a2 [0, 0, 0, 81, 702]  384

## Rank

sage: E.rank()

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

## Modular form1008.2.a.i

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 