# Properties

 Label 40560bz Number of curves $6$ Conductor $40560$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("40560.bx1")

sage: E.isogeny_class()

## Elliptic curves in class 40560bz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
40560.bx6 40560bz1 [0, 1, 0, 40504, -1243020] [2] 258048 $$\Gamma_0(N)$$-optimal
40560.bx5 40560bz2 [0, 1, 0, -175816, -10501516] [2, 2] 516096
40560.bx3 40560bz3 [0, 1, 0, -1527816, 719037684] [2, 2] 1032192
40560.bx2 40560bz4 [0, 1, 0, -2284936, -1329123340] [2] 1032192
40560.bx4 40560bz5 [0, 1, 0, -311016, 1834113204] [2] 2064384
40560.bx1 40560bz6 [0, 1, 0, -24376616, 46316102964] [2] 2064384

## Rank

sage: E.rank()

The elliptic curves in class 40560bz have rank $$1$$.

## Modular form 40560.2.a.bx

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} + q^{9} + 4q^{11} - q^{15} - 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.