Properties

 Label 4560.ba Number of curves $4$ Conductor $4560$ CM no Rank $0$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("ba1")

sage: E.isogeny_class()

Elliptic curves in class 4560.ba

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.ba1 4560j3 $$[0, 1, 0, -2440, -47212]$$ $$784767874322/35625$$ $$72960000$$ $$$$ $$3072$$ $$0.58494$$
4560.ba2 4560j4 $$[0, 1, 0, -760, 7220]$$ $$23735908082/1954815$$ $$4003461120$$ $$$$ $$3072$$ $$0.58494$$
4560.ba3 4560j2 $$[0, 1, 0, -160, -700]$$ $$445138564/81225$$ $$83174400$$ $$[2, 2]$$ $$1536$$ $$0.23837$$
4560.ba4 4560j1 $$[0, 1, 0, 20, -52]$$ $$3286064/7695$$ $$-1969920$$ $$$$ $$768$$ $$-0.10820$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 4560.ba have rank $$0$$.

Complex multiplication

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

Modular form4560.2.a.ba

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} + q^{9} - 4 q^{11} + 2 q^{13} + q^{15} + 6 q^{17} + q^{19} + O(q^{20})$$ 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 