# Properties

 Label 6720.bl Number of curves $6$ Conductor $6720$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("6720.bl1")

sage: E.isogeny_class()

## Elliptic curves in class 6720.bl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6720.bl1 6720q5 [0, 1, 0, -41921, -3317601]  16384
6720.bl2 6720q3 [0, 1, 0, -2721, -48321] [2, 2] 8192
6720.bl3 6720q2 [0, 1, 0, -721, 6479] [2, 2] 4096
6720.bl4 6720q1 [0, 1, 0, -701, 6915]  2048 $$\Gamma_0(N)$$-optimal
6720.bl5 6720q4 [0, 1, 0, 959, 33695]  8192
6720.bl6 6720q6 [0, 1, 0, 4479, -254241]  16384

## Rank

sage: E.rank()

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

## Modular form6720.2.a.bl

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} - q^{7} + q^{9} + 4q^{11} + 2q^{13} - q^{15} + 2q^{17} + 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 