# Properties

 Label 154560gk Number of curves $4$ Conductor $154560$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("gk1")

sage: E.isogeny_class()

## Elliptic curves in class 154560gk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
154560.du3 154560gk1 $$[0, -1, 0, -8135905, 9569257825]$$ $$-227196402372228188089/19338934824115200$$ $$-5069585730532854988800$$ $$[2]$$ $$8847360$$ $$2.9096$$ $$\Gamma_0(N)$$-optimal
154560.du2 154560gk2 $$[0, -1, 0, -132725985, 588589195617]$$ $$986396822567235411402169/6336721794060000$$ $$1661133597982064640000$$ $$[2]$$ $$17694720$$ $$3.2562$$
154560.du4 154560gk3 $$[0, -1, 0, 48234335, 337640737]$$ $$47342661265381757089751/27397579603968000000$$ $$-7182111107702587392000000$$ $$[2]$$ $$26542080$$ $$3.4589$$
154560.du1 154560gk4 $$[0, -1, 0, -192938145, 2894069025]$$ $$3029968325354577848895529/1753440696000000000000$$ $$459653957812224000000000000$$ $$[2]$$ $$53084160$$ $$3.8055$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 154560.2.a.gk

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} + q^{7} + q^{9} + 4q^{13} - q^{15} - 2q^{19} + O(q^{20})$$

## 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.