# Properties

 Label 1650.m Number of curves 4 Conductor 1650 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1650.m1")

sage: E.isogeny_class()

## Elliptic curves in class 1650.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1650.m1 1650m3 [1, 1, 1, -2013, -35469]  1728
1650.m2 1650m4 [1, 1, 1, -1013, -69469]  3456
1650.m3 1650m1 [1, 1, 1, -138, 531]  576 $$\Gamma_0(N)$$-optimal
1650.m4 1650m2 [1, 1, 1, 112, 2531]  1152

## Rank

sage: E.rank()

The elliptic curves in class 1650.m have rank $$0$$.

## Modular form1650.2.a.m

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 