# Properties

 Label 40560.bv Number of curves 8 Conductor 40560 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("40560.bv1")

sage: E.isogeny_class()

## Elliptic curves in class 40560.bv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
40560.bv1 40560ca8 [0, 1, 0, -5840696, 5431120020] [2] 589824
40560.bv2 40560ca6 [0, 1, 0, -365096, 84744180] [2, 2] 294912
40560.bv3 40560ca7 [0, 1, 0, -297496, 117165140] [2] 589824
40560.bv4 40560ca4 [0, 1, 0, -216376, -38812396] [2] 147456
40560.bv5 40560ca3 [0, 1, 0, -27096, 784980] [2, 2] 147456
40560.bv6 40560ca2 [0, 1, 0, -13576, -604876] [2, 2] 73728
40560.bv7 40560ca1 [0, 1, 0, -56, -26220] [2] 36864 $$\Gamma_0(N)$$-optimal
40560.bv8 40560ca5 [0, 1, 0, 94584, 5992884] [2] 294912

## Rank

sage: E.rank()

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

## Modular form 40560.2.a.bv

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} + q^{9} - 4q^{11} - q^{15} + 2q^{17} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.