# Properties

 Label 2790.v Number of curves $2$ Conductor $2790$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("v1")

E.isogeny_class()

## Elliptic curves in class 2790.v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2790.v1 2790x2 $$[1, -1, 1, -1966028, -1060550449]$$ $$1152829477932246539641/3188367360$$ $$2324319805440$$ $$[2]$$ $$33280$$ $$2.0310$$
2790.v2 2790x1 $$[1, -1, 1, -122828, -16561969]$$ $$-281115640967896441/468084326400$$ $$-341233473945600$$ $$[2]$$ $$16640$$ $$1.6845$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 2790.v have rank $$0$$.

## Complex multiplication

The elliptic curves in class 2790.v do not have complex multiplication.

## Modular form2790.2.a.v

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{5} + 4 q^{7} + q^{8} - q^{10} - 2 q^{11} + 2 q^{13} + 4 q^{14} + q^{16} + O(q^{20})$$

## 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.