# Properties

 Label 43350dd Number of curves 8 Conductor 43350 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("43350.cv1")

sage: E.isogeny_class()

## Elliptic curves in class 43350dd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
43350.cv8 43350dd1 [1, 0, 0, 10687, 1306617] [2] 221184 $$\Gamma_0(N)$$-optimal
43350.cv6 43350dd2 [1, 0, 0, -133813, 17057117] [2, 2] 442368
43350.cv7 43350dd3 [1, 0, 0, -97688, -38467008] [2] 663552
43350.cv5 43350dd4 [1, 0, 0, -495063, -115521633] [2] 884736
43350.cv4 43350dd5 [1, 0, 0, -2084563, 1158245867] [2] 884736
43350.cv3 43350dd6 [1, 0, 0, -2409688, -1437227008] [2, 2] 1327104
43350.cv1 43350dd7 [1, 0, 0, -38534688, -92074852008] [2] 2654208
43350.cv2 43350dd8 [1, 0, 0, -3276688, -310994008] [2] 2654208

## Rank

sage: E.rank()

The elliptic curves in class 43350dd have rank $$1$$.

## Modular form 43350.2.a.cv

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.