# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("630.c1")

sage: E.isogeny_class()

## Elliptic curves in class 630a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
630.c2 630a1 [1, -1, 0, -105, 441]  96 $$\Gamma_0(N)$$-optimal
630.c3 630a2 [1, -1, 0, -75, 675]  192
630.c1 630a3 [1, -1, 0, -420, -2800]  288
630.c4 630a4 [1, -1, 0, 660, -15544]  576

## Rank

sage: E.rank()

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

## Modular form630.2.a.c

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 Cremona 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 Cremona labels. 