# Properties

 Label 327990.n Number of curves $2$ Conductor $327990$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 327990.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
327990.n1 327990n1 $$[1, 0, 1, -8150149, -2926210384]$$ $$100654290922421809/52033093632000$$ $$30950497556090191872000$$ $$$$ $$32256000$$ $$3.0076$$ $$\Gamma_0(N)$$-optimal
327990.n2 327990n2 $$[1, 0, 1, 30603131, -22721385808]$$ $$5328847957372469711/3458851344000000$$ $$-2057405443283393424000000$$ $$$$ $$64512000$$ $$3.3542$$

## Rank

sage: E.rank()

The elliptic curves in class 327990.n have rank $$1$$.

## Complex multiplication

The elliptic curves in class 327990.n do not have complex multiplication.

## Modular form 327990.2.a.n

sage: E.q_eigenform(10)

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