# Properties

 Label 43350.bk Number of curves 6 Conductor 43350 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("43350.bk1")

sage: E.isogeny_class()

## Elliptic curves in class 43350.bk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
43350.bk1 43350ba6 [1, 0, 1, -200450551, -1092359612752] [2] 4718592
43350.bk2 43350ba4 [1, 0, 1, -12528301, -17068498252] [2, 2] 2359296
43350.bk3 43350ba5 [1, 0, 1, -11878051, -18919109752] [2] 4718592
43350.bk4 43350ba2 [1, 0, 1, -823801, -237427252] [2, 2] 1179648
43350.bk5 43350ba1 [1, 0, 1, -245801, 43480748] [2] 589824 $$\Gamma_0(N)$$-optimal
43350.bk6 43350ba3 [1, 0, 1, 1632699, -1382156252] [2] 2359296

## Rank

sage: E.rank()

The elliptic curves in class 43350.bk have rank $$0$$.

## Modular form 43350.2.a.bk

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.