# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("6720.g1")

sage: E.isogeny_class()

## Elliptic curves in class 6720a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6720.g4 6720a1 [0, -1, 0, 84, -4410]  3072 $$\Gamma_0(N)$$-optimal
6720.g3 6720a2 [0, -1, 0, -3561, -78039] [2, 2] 6144
6720.g1 6720a3 [0, -1, 0, -56481, -5147775]  12288
6720.g2 6720a4 [0, -1, 0, -8961, 221121]  12288

## Rank

sage: E.rank()

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

## Modular form6720.2.a.g

sage: E.q_eigenform(10)

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

## 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 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. 