# Properties

 Label 4290.y Number of curves $4$ Conductor $4290$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("y1")

sage: E.isogeny_class()

## Elliptic curves in class 4290.y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4290.y1 4290w3 $$[1, 0, 0, -160426, -24744844]$$ $$456612868287073618849/12544848030000$$ $$12544848030000$$ $$$$ $$24576$$ $$1.6167$$
4290.y2 4290w4 $$[1, 0, 0, -44746, 3289940]$$ $$9908022260084596129/1047363281250000$$ $$1047363281250000$$ $$$$ $$24576$$ $$1.6167$$
4290.y3 4290w2 $$[1, 0, 0, -10426, -354844]$$ $$125337052492018849/18404100000000$$ $$18404100000000$$ $$[2, 2]$$ $$12288$$ $$1.2702$$
4290.y4 4290w1 $$[1, 0, 0, 1094, -29980]$$ $$144794100308831/474439680000$$ $$-474439680000$$ $$$$ $$6144$$ $$0.92359$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 4290.y have rank $$0$$.

## Complex multiplication

The elliptic curves in class 4290.y do not have complex multiplication.

## Modular form4290.2.a.y

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{8} + q^{9} - q^{10} - q^{11} + q^{12} + q^{13} - q^{15} + q^{16} + 6q^{17} + q^{18} + 4q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 