# Properties

 Label 1290.m Number of curves $2$ Conductor $1290$ CM no Rank $1$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("m1")

sage: E.isogeny_class()

## Elliptic curves in class 1290.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1290.m1 1290m1 $$[1, 0, 0, -191, 921]$$ $$770842973809/66873600$$ $$66873600$$ $$[2]$$ $$640$$ $$0.24229$$ $$\Gamma_0(N)$$-optimal
1290.m2 1290m2 $$[1, 0, 0, 209, 4361]$$ $$1009328859791/8734528080$$ $$-8734528080$$ $$[2]$$ $$1280$$ $$0.58887$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1290.2.a.m

sage: E.q_eigenform(10)

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

## 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.