# Properties

 Label 59150bd Number of curves $4$ Conductor $59150$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("59150.bp1")

sage: E.isogeny_class()

## Elliptic curves in class 59150bd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
59150.bp4 59150bd1 [1, -1, 1, 9770, -594603]  184320 $$\Gamma_0(N)$$-optimal
59150.bp3 59150bd2 [1, -1, 1, -74730, -6340603] [2, 2] 368640
59150.bp2 59150bd3 [1, -1, 1, -370480, 81201397]  737280
59150.bp1 59150bd4 [1, -1, 1, -1130980, -462640603]  737280

## Rank

sage: E.rank()

The elliptic curves in class 59150bd have rank $$0$$.

## Modular form 59150.2.a.bp

sage: E.q_eigenform(10)

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

## 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. 