# Properties

 Label 80850i Number of curves 4 Conductor 80850 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("80850.m1")

sage: E.isogeny_class()

## Elliptic curves in class 80850i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
80850.m3 80850i1 [1, 1, 0, -613750, 160442500] [2] 1769472 $$\Gamma_0(N)$$-optimal
80850.m2 80850i2 [1, 1, 0, -2598250, -1452956000] [2, 2] 3538944
80850.m4 80850i3 [1, 1, 0, 3465500, -7219582250] [2] 7077888
80850.m1 80850i4 [1, 1, 0, -40414000, -98904143750] [2] 7077888

## Rank

sage: E.rank()

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

## Modular form 80850.2.a.m

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.