# Properties

 Label 84150.fo Number of curves 6 Conductor 84150 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("84150.fo1")

sage: E.isogeny_class()

## Elliptic curves in class 84150.fo

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
84150.fo1 84150fu6 [1, -1, 1, -65731505, 205112239247] [2] 9437184
84150.fo2 84150fu4 [1, -1, 1, -4475255, 2599076747] [2, 2] 4718592
84150.fo3 84150fu2 [1, -1, 1, -1662755, -792798253] [2, 2] 2359296
84150.fo4 84150fu1 [1, -1, 1, -1644755, -811482253] [2] 1179648 $$\Gamma_0(N)$$-optimal
84150.fo5 84150fu3 [1, -1, 1, 861745, -2989113253] [2] 4718592
84150.fo6 84150fu5 [1, -1, 1, 11780995, 17132164247] [2] 9437184

## Rank

sage: E.rank()

The elliptic curves in class 84150.fo have rank $$1$$.

## Modular form 84150.2.a.fo

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{8} + q^{11} - 6q^{13} + q^{16} + q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.