# Properties

 Label 4560ba Number of curves $2$ Conductor $4560$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 4560ba

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.bc2 4560ba1 $$[0, 1, 0, 0, 180]$$ $$-1/3420$$ $$-14008320$$ $$$$ $$1152$$ $$0.050147$$ $$\Gamma_0(N)$$-optimal
4560.bc1 4560ba2 $$[0, 1, 0, -480, 3828]$$ $$2992209121/54150$$ $$221798400$$ $$$$ $$2304$$ $$0.39672$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form4560.2.a.ba

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 