# Properties

 Label 6720.bh Number of curves $4$ Conductor $6720$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bh1")

sage: E.isogeny_class()

## Elliptic curves in class 6720.bh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6720.bh1 6720r3 $$[0, 1, 0, -336001, -75077185]$$ $$128025588102048008/7875$$ $$258048000$$ $$$$ $$24576$$ $$1.5225$$
6720.bh2 6720r4 $$[0, 1, 0, -23521, -880321]$$ $$43919722445768/15380859375$$ $$504000000000000$$ $$$$ $$24576$$ $$1.5225$$
6720.bh3 6720r2 $$[0, 1, 0, -21001, -1178185]$$ $$250094631024064/62015625$$ $$254016000000$$ $$[2, 2]$$ $$12288$$ $$1.1760$$
6720.bh4 6720r1 $$[0, 1, 0, -1156, -23206]$$ $$-2671731885376/1969120125$$ $$-126023688000$$ $$$$ $$6144$$ $$0.82939$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 6720.bh do not have complex multiplication.

## Modular form6720.2.a.bh

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} - q^{7} + q^{9} - 4q^{11} + 2q^{13} - q^{15} - 2q^{17} - 8q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 