# Properties

 Label 630.j Number of curves $4$ Conductor $630$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("630.j1")

sage: E.isogeny_class()

## Elliptic curves in class 630.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
630.j1 630h3 [1, -1, 1, -947, -10961]  288
630.j2 630h4 [1, -1, 1, -677, -17549]  576
630.j3 630h1 [1, -1, 1, -47, 119]  96 $$\Gamma_0(N)$$-optimal
630.j4 630h2 [1, -1, 1, 73, 551]  192

## Rank

sage: E.rank()

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

## Modular form630.2.a.j

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 