# Properties

 Label 630.d Number of curves $4$ Conductor $630$ CM no Rank $1$ Graph # Learn more

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

sage: E.isogeny_class()

## Elliptic curves in class 630.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
630.d1 630e4 $$[1, -1, 0, -2409, 46115]$$ $$2121328796049/120050$$ $$87516450$$ $$$$ $$512$$ $$0.58829$$
630.d2 630e3 $$[1, -1, 0, -789, -7777]$$ $$74565301329/5468750$$ $$3986718750$$ $$$$ $$512$$ $$0.58829$$
630.d3 630e2 $$[1, -1, 0, -159, 665]$$ $$611960049/122500$$ $$89302500$$ $$[2, 2]$$ $$256$$ $$0.24172$$
630.d4 630e1 $$[1, -1, 0, 21, 53]$$ $$1367631/2800$$ $$-2041200$$ $$$$ $$128$$ $$-0.10485$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 630.d have rank $$1$$.

## Complex multiplication

The elliptic curves in class 630.d do not have complex multiplication.

## Modular form630.2.a.d

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + q^{5} - q^{7} - q^{8} - q^{10} - 4q^{11} - 6q^{13} + q^{14} + q^{16} - 2q^{17} + O(q^{20})$$ ## 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. 