# Properties

 Label 1290.a Number of curves $2$ Conductor $1290$ CM no Rank $0$ Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 1290.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1290.a1 1290a2 $$[1, 1, 0, -507, -4611]$$ $$14457238157881/4437600$$ $$4437600$$ $$$$ $$480$$ $$0.25232$$
1290.a2 1290a1 $$[1, 1, 0, -27, -99]$$ $$-2305199161/1981440$$ $$-1981440$$ $$$$ $$240$$ $$-0.094250$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1290.a have rank $$0$$.

## Complex multiplication

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

## Modular form1290.2.a.a

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 