# Properties

 Label 4560.a Number of curves $4$ Conductor $4560$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 4560.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.a1 4560q4 $$[0, -1, 0, -19735096, 33751275376]$$ $$207530301091125281552569/805586668007040$$ $$3299682992156835840$$ $$[2]$$ $$215040$$ $$2.7666$$
4560.a2 4560q3 $$[0, -1, 0, -3740216, -2148427920]$$ $$1412712966892699019449/330160465517040000$$ $$1352337266757795840000$$ $$[2]$$ $$215040$$ $$2.7666$$
4560.a3 4560q2 $$[0, -1, 0, -1251896, 511088496]$$ $$52974743974734147769/3152005008998400$$ $$12910612516857446400$$ $$[2, 2]$$ $$107520$$ $$2.4200$$
4560.a4 4560q1 $$[0, -1, 0, 58824, 32937840]$$ $$5495662324535111/117739817533440$$ $$-482262292616970240$$ $$[2]$$ $$53760$$ $$2.0734$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form4560.2.a.a

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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.