# Properties

 Label 6720b Number of curves 2 Conductor 6720 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("6720.e1")

sage: E.isogeny_class()

## Elliptic curves in class 6720b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6720.e1 6720b1 [0, -1, 0, -21, 21]  768 $$\Gamma_0(N)$$-optimal
6720.e2 6720b2 [0, -1, 0, 79, 81]  1536

## Rank

sage: E.rank()

The elliptic curves in class 6720b have rank $$1$$.

## Modular form6720.2.a.e

sage: E.q_eigenform(10)

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

## 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 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. 