# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("40560.q1")

sage: E.isogeny_class()

## Elliptic curves in class 40560bv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
40560.q8 40560bv1 [0, -1, 0, 4000, -300288] [2] 110592 $$\Gamma_0(N)$$-optimal
40560.q6 40560bv2 [0, -1, 0, -50080, -3891200] [2, 2] 221184
40560.q7 40560bv3 [0, -1, 0, -36560, 8817600] [2] 331776
40560.q5 40560bv4 [0, -1, 0, -185280, 26501760] [2] 442368
40560.q4 40560bv5 [0, -1, 0, -780160, -264967808] [2] 442368
40560.q3 40560bv6 [0, -1, 0, -901840, 329317312] [2, 2] 663552
40560.q1 40560bv7 [0, -1, 0, -14421840, 21085221312] [2] 1327104
40560.q2 40560bv8 [0, -1, 0, -1226320, 71550400] [2] 1327104

## Rank

sage: E.rank()

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

## Modular form 40560.2.a.q

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.