# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

## Elliptic curves in class 14586.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14586.c1 14586b1 $$[1, 1, 0, -3020, -59376]$$ $$3047678972871625/304559880768$$ $$304559880768$$ $$$$ $$21504$$ $$0.93988$$ $$\Gamma_0(N)$$-optimal
14586.c2 14586b2 $$[1, 1, 0, 3740, -279752]$$ $$5783051584712375/37533175779528$$ $$-37533175779528$$ $$$$ $$43008$$ $$1.2865$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 14586.2.a.c

sage: E.q_eigenform(10)

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