Properties

 Label 4560.j Number of curves $4$ Conductor $4560$ CM no Rank $1$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("j1")

sage: E.isogeny_class()

Elliptic curves in class 4560.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.j1 4560f3 $$[0, -1, 0, -480, -3600]$$ $$11968836484/961875$$ $$984960000$$ $$$$ $$2048$$ $$0.46886$$
4560.j2 4560f2 $$[0, -1, 0, -100, 352]$$ $$436334416/81225$$ $$20793600$$ $$[2, 2]$$ $$1024$$ $$0.12229$$
4560.j3 4560f1 $$[0, -1, 0, -95, 390]$$ $$5988775936/285$$ $$4560$$ $$$$ $$512$$ $$-0.22429$$ $$\Gamma_0(N)$$-optimal
4560.j4 4560f4 $$[0, -1, 0, 200, 1792]$$ $$859687196/1954815$$ $$-2001730560$$ $$$$ $$2048$$ $$0.46886$$

Rank

sage: E.rank()

The elliptic curves in class 4560.j have rank $$1$$.

Complex multiplication

The elliptic curves in class 4560.j do not have complex multiplication.

Modular form4560.2.a.j

sage: E.q_eigenform(10)

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