# Properties

 Label 630d Number of curves $6$ Conductor $630$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("630.b1")

sage: E.isogeny_class()

## Elliptic curves in class 630d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
630.b6 630d1 [1, -1, 0, 90, 436] [2] 256 $$\Gamma_0(N)$$-optimal
630.b5 630d2 [1, -1, 0, -630, 4900] [2, 2] 512
630.b4 630d3 [1, -1, 0, -3330, -69080] [2] 1024
630.b2 630d4 [1, -1, 0, -9450, 355936] [2, 2] 1024
630.b1 630d5 [1, -1, 0, -151200, 22667386] [2] 2048
630.b3 630d6 [1, -1, 0, -8820, 404950] [2] 2048

## Rank

sage: E.rank()

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

## Modular form630.2.a.b

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{5} + q^{7} - q^{8} + q^{10} - 4q^{11} - 2q^{13} - q^{14} + q^{16} - 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.