Properties

 Label 18480bo Number of curves $4$ Conductor $18480$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bo1")

sage: E.isogeny_class()

Elliptic curves in class 18480bo

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18480.j3 18480bo1 $$[0, -1, 0, -2661, -52740]$$ $$-130287139815424/2250652635$$ $$-36010442160$$ $$[2]$$ $$20736$$ $$0.82354$$ $$\Gamma_0(N)$$-optimal
18480.j2 18480bo2 $$[0, -1, 0, -42756, -3388644]$$ $$33766427105425744/9823275$$ $$2514758400$$ $$[2]$$ $$41472$$ $$1.1701$$
18480.j4 18480bo3 $$[0, -1, 0, 10299, -260424]$$ $$7549996227362816/6152409907875$$ $$-98438558526000$$ $$[2]$$ $$62208$$ $$1.3728$$
18480.j1 18480bo4 $$[0, -1, 0, -49596, -2224980]$$ $$52702650535889104/22020583921875$$ $$5637269484000000$$ $$[2]$$ $$124416$$ $$1.7194$$

Rank

sage: E.rank()

The elliptic curves in class 18480bo have rank $$1$$.

Complex multiplication

The elliptic curves in class 18480bo do not have complex multiplication.

Modular form 18480.2.a.bo

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} - q^{7} + q^{9} + q^{11} + 2q^{13} + q^{15} - 6q^{17} - 8q^{19} + O(q^{20})$$

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.