# Properties

 Label 6720.f Number of curves $2$ Conductor $6720$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

## Elliptic curves in class 6720.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6720.f1 6720be2 $$[0, -1, 0, -841, 8041]$$ $$16079333824/2953125$$ $$12096000000$$ $$$$ $$4608$$ $$0.65316$$
6720.f2 6720be1 $$[0, -1, 0, 104, 670]$$ $$1925134784/4465125$$ $$-285768000$$ $$$$ $$2304$$ $$0.30659$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 6720.f have rank $$0$$.

## Complex multiplication

The elliptic curves in class 6720.f do not have complex multiplication.

## Modular form6720.2.a.f

sage: E.q_eigenform(10)

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

## 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. 