# Properties

 Label 14490.q Number of curves $2$ Conductor $14490$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("q1")

sage: E.isogeny_class()

## Elliptic curves in class 14490.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14490.q1 14490q1 $$[1, -1, 0, -2205, -37499]$$ $$1626794704081/83462400$$ $$60844089600$$ $$$$ $$24576$$ $$0.82718$$ $$\Gamma_0(N)$$-optimal
14490.q2 14490q2 $$[1, -1, 0, 1395, -150539]$$ $$411664745519/13605414480$$ $$-9918347155920$$ $$$$ $$49152$$ $$1.1738$$

## Rank

sage: E.rank()

The elliptic curves in class 14490.q have rank $$1$$.

## Complex multiplication

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

## Modular form 14490.2.a.q

sage: E.q_eigenform(10)

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