# Properties

 Label 6720g Number of curves 4 Conductor 6720 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("6720.p1")

sage: E.isogeny_class()

## Elliptic curves in class 6720g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6720.p3 6720g1 [0, -1, 0, -161, 801]  2048 $$\Gamma_0(N)$$-optimal
6720.p2 6720g2 [0, -1, 0, -481, -2975] [2, 2] 4096
6720.p1 6720g3 [0, -1, 0, -7201, -232799]  8192
6720.p4 6720g4 [0, -1, 0, 1119, -19935]  8192

## Rank

sage: E.rank()

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

## Modular form6720.2.a.p

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 Cremona 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 Cremona labels. 