# Properties

 Label 6720.bk Number of curves 4 Conductor 6720 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("6720.bk1")

sage: E.isogeny_class()

## Elliptic curves in class 6720.bk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6720.bk1 6720bx3 [0, 1, 0, -7201, 232799]  8192
6720.bk2 6720bx2 [0, 1, 0, -481, 2975] [2, 2] 4096
6720.bk3 6720bx1 [0, 1, 0, -161, -801]  2048 $$\Gamma_0(N)$$-optimal
6720.bk4 6720bx4 [0, 1, 0, 1119, 19935]  8192

## Rank

sage: E.rank()

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

## Modular form6720.2.a.bk

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} - q^{7} + q^{9} + 6q^{13} - q^{15} + 2q^{17} - 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 