# Properties

 Label 210.d Number of curves 8 Conductor 210 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("210.d1")
sage: E.isogeny_class()

## Elliptic curves in class 210.d

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
210.d1 210a7 [1, 0, 0, -6451, 124931] 2 576
210.d2 210a4 [1, 0, 0, -5761, 167825] 6 192
210.d3 210a6 [1, 0, 0, -2701, -52819] 4 288
210.d4 210a3 [1, 0, 0, -2681, -53655] 2 144
210.d5 210a2 [1, 0, 0, -361, 2585] 12 96
210.d6 210a5 [1, 0, 0, -81, 6561] 6 192
210.d7 210a1 [1, 0, 0, -41, -39] 6 48 $$\Gamma_0(N)$$-optimal
210.d8 210a8 [1, 0, 0, 729, -176985] 2 576

## Rank

sage: E.rank()

The elliptic curves in class 210.d have rank $$0$$.

## Modular form210.2.a.d

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.