# Properties

 Label 1470.d Number of curves 8 Conductor 1470 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1470.d1")

sage: E.isogeny_class()

## Elliptic curves in class 1470.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1470.d1 1470d8 [1, 1, 0, -261342, 51314796] [2] 6912
1470.d2 1470d7 [1, 1, 0, -22222, 164284] [2] 6912
1470.d3 1470d6 [1, 1, 0, -16342, 795796] [2, 2] 3456
1470.d4 1470d4 [1, 1, 0, -14137, -652889] [2] 2304
1470.d5 1470d5 [1, 1, 0, -3357, 63099] [2] 2304
1470.d6 1470d2 [1, 1, 0, -907, -9911] [2, 2] 1152
1470.d7 1470d3 [1, 1, 0, -662, 21204] [2] 1728
1470.d8 1470d1 [1, 1, 0, 73, -699] [2] 576 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1470.d have rank $$1$$.

## Modular form1470.2.a.d

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 12 & 3 & 6 & 4 & 12 \\ 4 & 1 & 2 & 3 & 12 & 6 & 4 & 12 \\ 2 & 2 & 1 & 6 & 6 & 3 & 2 & 6 \\ 12 & 3 & 6 & 1 & 4 & 2 & 12 & 4 \\ 3 & 12 & 6 & 4 & 1 & 2 & 12 & 4 \\ 6 & 6 & 3 & 2 & 2 & 1 & 6 & 2 \\ 4 & 4 & 2 & 12 & 12 & 6 & 1 & 3 \\ 12 & 12 & 6 & 4 & 4 & 2 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.