# Properties

 Label 6720be Number of curves 2 Conductor 6720 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("6720.f1")

sage: E.isogeny_class()

## Elliptic curves in class 6720be

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6720.f2 6720be1 [0, -1, 0, 104, 670]  2304 $$\Gamma_0(N)$$-optimal
6720.f1 6720be2 [0, -1, 0, -841, 8041]  4608

## Rank

sage: E.rank()

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

## Modular form6720.2.a.f

sage: E.q_eigenform(10)

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

## 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. 