# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("6720.c1")

sage: E.isogeny_class()

## Elliptic curves in class 6720bi

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6720.c4 6720bi1 [0, -1, 0, -1600156, -768989294]  215040 $$\Gamma_0(N)$$-optimal
6720.c2 6720bi2 [0, -1, 0, -25515001, -49598319815] [2, 2] 430080
6720.c1 6720bi3 [0, -1, 0, -408240001, -3174701034815]  860160
6720.c3 6720bi4 [0, -1, 0, -25427521, -49955395679]  860160

## Rank

sage: E.rank()

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

## Modular form6720.2.a.c

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 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. 