# Properties

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

Show commands: SageMath
E = EllipticCurve("d1")

E.isogeny_class()

## Elliptic curves in class 510.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
510.d1 510c2 $$[1, 1, 1, -156, 603]$$ $$420021471169/50191650$$ $$50191650$$ $$$$ $$160$$ $$0.20855$$
510.d2 510c1 $$[1, 1, 1, 14, 59]$$ $$302111711/1404540$$ $$-1404540$$ $$$$ $$80$$ $$-0.13802$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form510.2.a.d

sage: E.q_eigenform(10)

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

## 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. 