# Properties

 Label 14490.n Number of curves $2$ Conductor $14490$ CM no Rank $0$ Graph # Learn more

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

sage: E.isogeny_class()

## Elliptic curves in class 14490.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14490.n1 14490b1 $$[1, -1, 0, -1275, -16875]$$ $$8493409990827/185150000$$ $$4999050000$$ $$$$ $$10240$$ $$0.64932$$ $$\Gamma_0(N)$$-optimal
14490.n2 14490b2 $$[1, -1, 0, 105, -52479]$$ $$4716275733/44023437500$$ $$-1188632812500$$ $$$$ $$20480$$ $$0.99590$$

## Rank

sage: E.rank()

The elliptic curves in class 14490.n have rank $$0$$.

## Complex multiplication

The elliptic curves in class 14490.n do not have complex multiplication.

## Modular form 14490.2.a.n

sage: E.q_eigenform(10)

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