# Properties

 Label 55506bd Number of curves 4 Conductor 55506 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("55506.ba1")

sage: E.isogeny_class()

## Elliptic curves in class 55506bd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
55506.ba3 55506bd1 [1, 1, 1, -4643, 112925] [2] 96768 $$\Gamma_0(N)$$-optimal
55506.ba4 55506bd2 [1, 1, 1, 3767, 486329] [2] 193536
55506.ba1 55506bd3 [1, 1, 1, -67718, -6784957] [2] 290304
55506.ba2 55506bd4 [1, 1, 1, -34078, -13486045] [2] 580608

## Rank

sage: E.rank()

The elliptic curves in class 55506bd have rank $$1$$.

## Modular form 55506.2.a.ba

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} - q^{6} + 2q^{7} + q^{8} + q^{9} + q^{11} - q^{12} - 4q^{13} + 2q^{14} + q^{16} + 6q^{17} + q^{18} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.