# Properties

 Label 14586g Number of curves $2$ Conductor $14586$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 14586g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14586.h1 14586g1 $$[1, 0, 1, -94, -256]$$ $$90458382169/25788048$$ $$25788048$$ $$$$ $$6400$$ $$0.12875$$ $$\Gamma_0(N)$$-optimal
14586.h2 14586g2 $$[1, 0, 1, 246, -1616]$$ $$1656015369191/2114999172$$ $$-2114999172$$ $$$$ $$12800$$ $$0.47533$$

## Rank

sage: E.rank()

The elliptic curves in class 14586g have rank $$0$$.

## Complex multiplication

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

## Modular form 14586.2.a.g

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels. 