# Properties

 Label 630j Number of curves $4$ Conductor $630$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("j1")

sage: E.isogeny_class()

## Elliptic curves in class 630j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
630.i3 630j1 [1, -1, 1, -32, 51] [4] 128 $$\Gamma_0(N)$$-optimal
630.i2 630j2 [1, -1, 1, -212, -1101] [2, 2] 256
630.i1 630j3 [1, -1, 1, -3362, -74181] [2] 512
630.i4 630j4 [1, -1, 1, 58, -3909] [2] 512

## Rank

sage: E.rank()

The elliptic curves in class 630j have rank $$0$$.

## Complex multiplication

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

## Modular form630.2.a.j

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.