# Properties

 Label 63063.w Number of curves $6$ Conductor $63063$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("63063.w1")

sage: E.isogeny_class()

## Elliptic curves in class 63063.w

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
63063.w1 63063t4 [1, -1, 0, -3027033, 2027850754] [2] 786432
63063.w2 63063t6 [1, -1, 0, -1326978, -569398019] [2] 1572864
63063.w3 63063t3 [1, -1, 0, -209043, 24672640] [2, 2] 786432
63063.w4 63063t2 [1, -1, 0, -189198, 31717615] [2, 2] 393216
63063.w5 63063t1 [1, -1, 0, -10593, 604624] [2] 196608 $$\Gamma_0(N)$$-optimal
63063.w6 63063t5 [1, -1, 0, 591372, 167626759] [2] 1572864

## Rank

sage: E.rank()

The elliptic curves in class 63063.w have rank $$0$$.

## Modular form 63063.2.a.w

sage: E.q_eigenform(10)

$$q + q^{2} - q^{4} - 2q^{5} - 3q^{8} - 2q^{10} + q^{11} - q^{13} - q^{16} - 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.