# Properties

 Label 14586.d Number of curves $2$ Conductor $14586$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

## Elliptic curves in class 14586.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14586.d1 14586f1 $$[1, 0, 1, -39458, 2580212]$$ $$6793805286030262681/1048227429629952$$ $$1048227429629952$$ $$$$ $$150528$$ $$1.6056$$ $$\Gamma_0(N)$$-optimal
14586.d2 14586f2 $$[1, 0, 1, 68702, 14261492]$$ $$35862531227445945959/108547797844556928$$ $$-108547797844556928$$ $$$$ $$301056$$ $$1.9522$$

## Rank

sage: E.rank()

The elliptic curves in class 14586.d have rank $$1$$.

## Complex multiplication

The elliptic curves in class 14586.d do not have complex multiplication.

## Modular form 14586.2.a.d

sage: E.q_eigenform(10)

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