# Properties

 Label 2790l Number of curves $4$ Conductor $2790$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

## Elliptic curves in class 2790l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2790.k4 2790l1 $$[1, -1, 0, 12501, 600453]$$ $$296354077829711/387386634240$$ $$-282404856360960$$ $$[2]$$ $$11520$$ $$1.4587$$ $$\Gamma_0(N)$$-optimal
2790.k3 2790l2 $$[1, -1, 0, -76779, 5903685]$$ $$68663623745397169/19216056254400$$ $$14008505009457600$$ $$[2]$$ $$23040$$ $$1.8053$$
2790.k2 2790l3 $$[1, -1, 0, -356859, 82633365]$$ $$-6894246873502147249/47925198774000$$ $$-34937469906246000$$ $$[6]$$ $$34560$$ $$2.0081$$
2790.k1 2790l4 $$[1, -1, 0, -5719239, 5265909873]$$ $$28379906689597370652529/1357352437500$$ $$989509926937500$$ $$[6]$$ $$69120$$ $$2.3546$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form2790.2.a.l

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + q^{5} + 2 q^{7} - q^{8} - q^{10} - 4 q^{13} - 2 q^{14} + q^{16} - 6 q^{17} + 8 q^{19} + O(q^{20})$$

## 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 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.