# Properties

 Label 154560.eh Number of curves $4$ Conductor $154560$ CM no Rank $2$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("eh1")

sage: E.isogeny_class()

## Elliptic curves in class 154560.eh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
154560.eh1 154560bu3 $$[0, 1, 0, -741921, 245724255]$$ $$344577854816148242/2716875$$ $$356106240000$$ $$[2]$$ $$983040$$ $$1.8075$$
154560.eh2 154560bu2 $$[0, 1, 0, -46401, 3822399]$$ $$168591300897604/472410225$$ $$30959876505600$$ $$[2, 2]$$ $$491520$$ $$1.4609$$
154560.eh3 154560bu4 $$[0, 1, 0, -28001, 6902559]$$ $$-18524646126002/146738831715$$ $$-19233352150548480$$ $$[2]$$ $$983040$$ $$1.8075$$
154560.eh4 154560bu1 $$[0, 1, 0, -4081, 5135]$$ $$458891455696/264449745$$ $$4332744622080$$ $$[2]$$ $$245760$$ $$1.1143$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 154560.eh have rank $$2$$.

## Complex multiplication

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

## Modular form 154560.2.a.eh

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.