# Properties

 Label 1290n Number of curves $4$ Conductor $1290$ CM no Rank $0$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

## Elliptic curves in class 1290n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1290.n2 1290n1 $$[1, 0, 0, -17566, 894596]$$ $$599437478278595809/33854760000$$ $$33854760000$$ $$[6]$$ $$2880$$ $$1.0849$$ $$\Gamma_0(N)$$-optimal
1290.n3 1290n2 $$[1, 0, 0, -16566, 1001196]$$ $$-502780379797811809/143268096832200$$ $$-143268096832200$$ $$[6]$$ $$5760$$ $$1.4315$$
1290.n1 1290n3 $$[1, 0, 0, -34306, -1065280]$$ $$4465136636671380769/2096375976562500$$ $$2096375976562500$$ $$[2]$$ $$8640$$ $$1.6342$$
1290.n4 1290n4 $$[1, 0, 0, 121944, -8034030]$$ $$200541749524551119231/144008551960031250$$ $$-144008551960031250$$ $$[2]$$ $$17280$$ $$1.9808$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1290.2.a.n

sage: E.q_eigenform(10)

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

## 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.