# Properties

 Label 6720.a Number of curves 4 Conductor 6720 CM no Rank 2 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("6720.a1")

sage: E.isogeny_class()

## Elliptic curves in class 6720.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6720.a1 6720bj3 [0, -1, 0, -4481, 116961] [2] 6144
6720.a2 6720bj2 [0, -1, 0, -281, 1881] [2, 2] 3072
6720.a3 6720bj1 [0, -1, 0, -36, -30] [2] 1536 $$\Gamma_0(N)$$-optimal
6720.a4 6720bj4 [0, -1, 0, -1, 5185] [2] 6144

## Rank

sage: E.rank()

The elliptic curves in class 6720.a have rank $$2$$.

## Modular form6720.2.a.a

sage: E.q_eigenform(10)

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

## 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.