# Properties

 Label 80850.fq Number of curves 4 Conductor 80850 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("80850.fq1")

sage: E.isogeny_class()

## Elliptic curves in class 80850.fq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
80850.fq1 80850gb3 [1, 0, 0, -98638, 11869892]  622080
80850.fq2 80850gb4 [1, 0, 0, -49638, 23678892]  1244160
80850.fq3 80850gb1 [1, 0, 0, -6763, -202483]  207360 $$\Gamma_0(N)$$-optimal
80850.fq4 80850gb2 [1, 0, 0, 5487, -851733]  414720

## Rank

sage: E.rank()

The elliptic curves in class 80850.fq have rank $$0$$.

## Modular form 80850.2.a.fq

sage: E.q_eigenform(10)

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

## 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. 