# Properties

 Label 2790.p Number of curves $2$ Conductor $2790$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("p1")

sage: E.isogeny_class()

## Elliptic curves in class 2790.p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2790.p1 2790t2 $$[1, -1, 1, -18113, 333281]$$ $$901456690969801/457629750000$$ $$333612087750000$$ $$$$ $$15360$$ $$1.4792$$
2790.p2 2790t1 $$[1, -1, 1, 4207, 38657]$$ $$11298232190519/7472736000$$ $$-5447624544000$$ $$$$ $$7680$$ $$1.1326$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 2790.p have rank $$1$$.

## Complex multiplication

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

## Modular form2790.2.a.p

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{5} - 2 q^{7} + q^{8} - q^{10} + 4 q^{11} - 4 q^{13} - 2 q^{14} + q^{16} - 2 q^{17} - 8 q^{19} + O(q^{20})$$

## 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. 