# Properties

 Label 6630q Number of curves 2 Conductor 6630 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("6630.s1")

sage: E.isogeny_class()

## Elliptic curves in class 6630q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6630.s1 6630q1 [1, 1, 1, -13620, 599157]  15360 $$\Gamma_0(N)$$-optimal
6630.s2 6630q2 [1, 1, 1, -2100, 1594485]  30720

## Rank

sage: E.rank()

The elliptic curves in class 6630q have rank $$1$$.

## Modular form6630.2.a.s

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} - 2q^{7} + q^{8} + q^{9} + q^{10} - q^{12} - q^{13} - 2q^{14} - q^{15} + q^{16} - q^{17} + q^{18} + 2q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 