# Properties

 Label 10647.d Number of curves 6 Conductor 10647 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("10647.d1")

sage: E.isogeny_class()

## Elliptic curves in class 10647.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
10647.d1 10647f5 [1, -1, 1, -1192496, 501523832] [2] 73728
10647.d2 10647f4 [1, -1, 1, -74561, 7843736] [2, 2] 36864
10647.d3 10647f3 [1, -1, 1, -59351, -5516728] [2] 36864
10647.d4 10647f6 [1, -1, 1, -51746, 12717020] [2] 73728
10647.d5 10647f2 [1, -1, 1, -6116, 41006] [2, 2] 18432
10647.d6 10647f1 [1, -1, 1, 1489, 4502] [2] 9216 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 10647.d have rank $$1$$.

## Modular form 10647.2.a.d

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.