# Properties

 Label 154560.bv Number of curves $4$ Conductor $154560$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bv1")

sage: E.isogeny_class()

## Elliptic curves in class 154560.bv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
154560.bv1 154560hn4 $$[0, -1, 0, -741921, -245724255]$$ $$344577854816148242/2716875$$ $$356106240000$$ $$$$ $$983040$$ $$1.8075$$
154560.bv2 154560hn2 $$[0, -1, 0, -46401, -3822399]$$ $$168591300897604/472410225$$ $$30959876505600$$ $$[2, 2]$$ $$491520$$ $$1.4609$$
154560.bv3 154560hn3 $$[0, -1, 0, -28001, -6902559]$$ $$-18524646126002/146738831715$$ $$-19233352150548480$$ $$$$ $$983040$$ $$1.8075$$
154560.bv4 154560hn1 $$[0, -1, 0, -4081, -5135]$$ $$458891455696/264449745$$ $$4332744622080$$ $$$$ $$245760$$ $$1.1143$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 154560.bv have rank $$0$$.

## Complex multiplication

The elliptic curves in class 154560.bv do not have complex multiplication.

## Modular form 154560.2.a.bv

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + q^{7} + q^{9} + 4 q^{11} - 2 q^{13} + q^{15} - 2 q^{17} + 4 q^{19} + O(q^{20})$$ ## 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 LMFDB 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 LMFDB labels. 