# Properties

 Label 50820m Number of curves $4$ Conductor $50820$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 50820m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
50820.m3 50820m1 $$[0, 1, 0, -322021, -71484976]$$ $$-130287139815424/2250652635$$ $$-63794694923411760$$ $$$$ $$622080$$ $$2.0225$$ $$\Gamma_0(N)$$-optimal
50820.m2 50820m2 $$[0, 1, 0, -5173516, -4530979180]$$ $$33766427105425744/9823275$$ $$4455047905862400$$ $$$$ $$1244160$$ $$2.3691$$
50820.m4 50820m3 $$[0, 1, 0, 1246139, -341639740]$$ $$7549996227362816/6152409907875$$ $$-174389911180879086000$$ $$$$ $$1866240$$ $$2.5718$$
50820.m1 50820m4 $$[0, 1, 0, -6001156, -2985452956]$$ $$52702650535889104/22020583921875$$ $$9986766764344524000000$$ $$$$ $$3732480$$ $$2.9184$$

## Rank

sage: E.rank()

The elliptic curves in class 50820m have rank $$0$$.

## Complex multiplication

The elliptic curves in class 50820m do not have complex multiplication.

## Modular form 50820.2.a.m

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} - q^{7} + q^{9} - 2q^{13} - q^{15} + 6q^{17} - 8q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 