# Properties

 Label 308550.do Number of curves $2$ Conductor $308550$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("do1")

sage: E.isogeny_class()

## Elliptic curves in class 308550.do

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
308550.do1 308550do2 $$[1, 0, 1, -434151, -70367552]$$ $$326940373369/112003650$$ $$3100332784338281250$$ $$[2]$$ $$5898240$$ $$2.2501$$
308550.do2 308550do1 $$[1, 0, 1, 80099, -7629052]$$ $$2053225511/2098140$$ $$-58077859320937500$$ $$[2]$$ $$2949120$$ $$1.9035$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 308550.do have rank $$0$$.

## Complex multiplication

The elliptic curves in class 308550.do do not have complex multiplication.

## Modular form 308550.2.a.do

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{6} - 2q^{7} - q^{8} + q^{9} + q^{12} + 2q^{14} + q^{16} + q^{17} - q^{18} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.