# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("6720.h1")

sage: E.isogeny_class()

## Elliptic curves in class 6720.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6720.h1 6720bh5 [0, -1, 0, -97601, 11765985]  32768
6720.h2 6720bh3 [0, -1, 0, -6881, 135681] [2, 2] 16384
6720.h3 6720bh2 [0, -1, 0, -2961, -59535] [2, 2] 8192
6720.h4 6720bh1 [0, -1, 0, -2941, -60419]  4096 $$\Gamma_0(N)$$-optimal
6720.h5 6720bh4 [0, -1, 0, 639, -198495]  16384
6720.h6 6720bh6 [0, -1, 0, 21119, 936481]  32768

## Rank

sage: E.rank()

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

## Modular form6720.2.a.h

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} - q^{7} + q^{9} + 4q^{11} + 2q^{13} + q^{15} - 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 