# Properties

 Label 40656bk Number of curves 6 Conductor 40656 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("40656.l1")

sage: E.isogeny_class()

## Elliptic curves in class 40656bk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
40656.l6 40656bk1 [0, -1, 0, 1896, -7632] [2] 40960 $$\Gamma_0(N)$$-optimal
40656.l5 40656bk2 [0, -1, 0, -7784, -54096] [2, 2] 81920
40656.l3 40656bk3 [0, -1, 0, -75544, 7968688] [2] 163840
40656.l2 40656bk4 [0, -1, 0, -94904, -11205456] [2, 2] 163840
40656.l4 40656bk5 [0, -1, 0, -65864, -18221520] [2] 327680
40656.l1 40656bk6 [0, -1, 0, -1517864, -719270352] [2] 327680

## Rank

sage: E.rank()

The elliptic curves in class 40656bk have rank $$1$$.

## Modular form 40656.2.a.l

sage: E.q_eigenform(10)

$$q - q^{3} - 2q^{5} - q^{7} + q^{9} + 2q^{13} + 2q^{15} + 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.