# Properties

 Label 43560q Number of curves 4 Conductor 43560 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("43560.bd1")

sage: E.isogeny_class()

## Elliptic curves in class 43560q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
43560.bd3 43560q1 [0, 0, 0, -2178, 35937] [2] 40960 $$\Gamma_0(N)$$-optimal
43560.bd2 43560q2 [0, 0, 0, -7623, -215622] [2, 2] 81920
43560.bd4 43560q3 [0, 0, 0, 14157, -1221858] [2] 163840
43560.bd1 43560q4 [0, 0, 0, -116523, -15309162] [2] 163840

## Rank

sage: E.rank()

The elliptic curves in class 43560q have rank $$1$$.

## Modular form 43560.2.a.bd

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.