# Properties

 Label 43890.ct Number of curves 8 Conductor 43890 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("43890.ct1")
sage: E.isogeny_class()

## Elliptic curves in class 43890.ct

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
43890.ct1 43890ct7 [1, 0, 0, -150608156, -711423835980] 2 5971968
43890.ct2 43890ct8 [1, 0, 0, -18882436, 14644625516] 2 5971968
43890.ct3 43890ct5 [1, 0, 0, -15906496, 24416653760] 6 1990656
43890.ct4 43890ct6 [1, 0, 0, -9449936, -11024979984] 4 2985984
43890.ct5 43890ct4 [1, 0, 0, -2148416, -652538304] 6 1990656
43890.ct6 43890ct2 [1, 0, 0, -999296, 377303040] 12 995328
43890.ct7 43890ct3 [1, 0, 0, -38016, -481747200] 2 1492992
43890.ct8 43890ct1 [1, 0, 0, 4224, 17842176] 6 497664 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 43890.ct have rank $$0$$.

## Modular form None

sage: E.q_eigenform(10)
$$q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{7} + q^{8} + q^{9} - q^{10} + q^{11} + q^{12} + 2q^{13} + q^{14} - q^{15} + q^{16} + 6q^{17} + q^{18} + q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.