# Properties

 Label 76664.e Number of curves $2$ Conductor $76664$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

## Elliptic curves in class 76664.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
76664.e1 76664c1 $$[0, 0, 0, -23111458, -42765061575]$$ $$33256413948450816/2481997$$ $$101890003999340368$$ $$$$ $$3348864$$ $$2.7132$$ $$\Gamma_0(N)$$-optimal
76664.e2 76664c2 $$[0, 0, 0, -23063543, -42951211350]$$ $$-2065624967846736/17960084863$$ $$-11796649994465343223552$$ $$$$ $$6697728$$ $$3.0598$$

## Rank

sage: E.rank()

The elliptic curves in class 76664.e have rank $$1$$.

## Complex multiplication

The elliptic curves in class 76664.e do not have complex multiplication.

## Modular form 76664.2.a.e

sage: E.q_eigenform(10)

$$q + 4q^{5} - q^{7} - 3q^{9} - 4q^{11} + 4q^{13} - 2q^{19} + O(q^{20})$$ ## 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 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. 