# Properties

 Label 799.a Number of curves $2$ Conductor $799$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("a1")

E.isogeny_class()

## Elliptic curves in class 799.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
799.a1 799b2 $$[1, 1, 1, -353, -2120]$$ $$4865469108625/1134465743$$ $$1134465743$$ $$$$ $$336$$ $$0.44939$$
799.a2 799b1 $$[1, 1, 1, -118, 418]$$ $$181802454625/10852817$$ $$10852817$$ $$$$ $$168$$ $$0.10282$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 799.a have rank $$1$$.

## Complex multiplication

The elliptic curves in class 799.a do not have complex multiplication.

## Modular form799.2.a.a

sage: E.q_eigenform(10)

$$q - q^{2} + 2 q^{3} - q^{4} - 2 q^{6} - 2 q^{7} + 3 q^{8} + q^{9} - 2 q^{12} - 6 q^{13} + 2 q^{14} - q^{16} + q^{17} - q^{18} - 4 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 