# Properties

 Label 185900bd Number of curves 4 Conductor 185900 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("185900.bb1")

sage: E.isogeny_class()

## Elliptic curves in class 185900bd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
185900.bb4 185900bd1 [0, -1, 0, -191533, 31666062] [2] 1866240 $$\Gamma_0(N)$$-optimal
185900.bb3 185900bd2 [0, -1, 0, -423908, -59889688] [2] 3732480
185900.bb2 185900bd3 [0, -1, 0, -1881533, -980221438] [2] 5598720
185900.bb1 185900bd4 [0, -1, 0, -29998908, -63232089688] [2] 11197440

## Rank

sage: E.rank()

The elliptic curves in class 185900bd have rank $$1$$.

## Modular form 185900.2.a.bb

sage: E.q_eigenform(10)

$$q + 2q^{3} - 4q^{7} + q^{9} + q^{11} + 4q^{19} + O(q^{20})$$

## 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.