# Properties

 Label 510.a Number of curves $2$ Conductor $510$ CM no Rank $0$ Graph # Related objects

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

E.isogeny_class()

## Elliptic curves in class 510.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
510.a1 510a2 $$[1, 1, 0, -46193, 3801813]$$ $$10901014250685308569/1040774054400$$ $$1040774054400$$ $$$$ $$2016$$ $$1.3426$$
510.a2 510a1 $$[1, 1, 0, -2673, 67797]$$ $$-2113364608155289/828431400960$$ $$-828431400960$$ $$$$ $$1008$$ $$0.99603$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 510.a have rank $$0$$.

## Complex multiplication

The elliptic curves in class 510.a do not have complex multiplication.

## Modular form510.2.a.a

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} + 2 q^{7} - q^{8} + q^{9} + q^{10} - 4 q^{11} - q^{12} + 4 q^{13} - 2 q^{14} + q^{15} + q^{16} + q^{17} - q^{18} - 4 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 