# Properties

 Label 6630s Number of curves 4 Conductor 6630 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("6630.t1")

sage: E.isogeny_class()

## Elliptic curves in class 6630s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6630.t4 6630s1 [1, 1, 1, 1580, 4757]  11520 $$\Gamma_0(N)$$-optimal
6630.t3 6630s2 [1, 1, 1, -6420, 30357] [2, 2] 23040
6630.t2 6630s3 [1, 1, 1, -64220, -6258283]  46080
6630.t1 6630s4 [1, 1, 1, -76620, 8117397]  46080

## Rank

sage: E.rank()

The elliptic curves in class 6630s have rank $$0$$.

## Modular form6630.2.a.t

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + 4q^{7} + q^{8} + q^{9} + q^{10} - 4q^{11} - q^{12} + q^{13} + 4q^{14} - q^{15} + q^{16} - q^{17} + q^{18} + 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 