# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("cb1")

sage: E.isogeny_class()

## Elliptic curves in class 6720cb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6720.bx4 6720cb1 $$[0, 1, 0, -1600156, 768989294]$$ $$7079962908642659949376/100085966990454375$$ $$6405501887389080000$$ $$$$ $$215040$$ $$2.4134$$ $$\Gamma_0(N)$$-optimal
6720.bx2 6720cb2 $$[0, 1, 0, -25515001, 49598319815]$$ $$448487713888272974160064/91549016015625$$ $$374984769600000000$$ $$[2, 2]$$ $$430080$$ $$2.7600$$
6720.bx1 6720cb3 $$[0, 1, 0, -408240001, 3174701034815]$$ $$229625675762164624948320008/9568125$$ $$313528320000$$ $$$$ $$860160$$ $$3.1066$$
6720.bx3 6720cb4 $$[0, 1, 0, -25427521, 49955395679]$$ $$-55486311952875723077768/801237030029296875$$ $$-26254935000000000000000$$ $$$$ $$860160$$ $$3.1066$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form6720.2.a.cb

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. 