# Properties

 Label 1290.g Number of curves $2$ Conductor $1290$ CM no Rank $1$ Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 1290.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1290.g1 1290f2 $$[1, 0, 1, -238, -1384]$$ $$1481933914201/53916840$$ $$53916840$$ $$$$ $$576$$ $$0.25331$$
1290.g2 1290f1 $$[1, 0, 1, -38, 56]$$ $$5841725401/1857600$$ $$1857600$$ $$$$ $$288$$ $$-0.093268$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1290.g have rank $$1$$.

## Complex multiplication

The elliptic curves in class 1290.g do not have complex multiplication.

## Modular form1290.2.a.g

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - 2q^{7} - q^{8} + q^{9} - q^{10} - 2q^{11} + q^{12} - 2q^{13} + 2q^{14} + q^{15} + q^{16} - 4q^{17} - q^{18} - 6q^{19} + O(q^{20})$$ ## 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. 