# Properties

 Label 76664.j Number of curves $2$ Conductor $76664$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("j1")

sage: E.isogeny_class()

## Elliptic curves in class 76664.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
76664.j1 76664i2 $$[0, -1, 0, -2004672, -1067303380]$$ $$169556172914/4353013$$ $$22873375565456009216$$ $$$$ $$2363904$$ $$2.4969$$
76664.j2 76664i1 $$[0, -1, 0, 21448, -53432932]$$ $$415292/469567$$ $$-1233695183559580672$$ $$$$ $$1181952$$ $$2.1504$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 76664.j have rank $$0$$.

## Complex multiplication

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

## Modular form 76664.2.a.j

sage: E.q_eigenform(10)

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