Properties

 Label 6720cc Number of curves $4$ Conductor $6720$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cc1")

sage: E.isogeny_class()

Elliptic curves in class 6720cc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6720.bv3 6720cc1 $$[0, 1, 0, -36, 30]$$ $$82881856/36015$$ $$2304960$$ $$[2]$$ $$1536$$ $$-0.082988$$ $$\Gamma_0(N)$$-optimal
6720.bv2 6720cc2 $$[0, 1, 0, -281, -1881]$$ $$601211584/11025$$ $$45158400$$ $$[2, 2]$$ $$3072$$ $$0.26359$$
6720.bv1 6720cc3 $$[0, 1, 0, -4481, -116961]$$ $$303735479048/105$$ $$3440640$$ $$[2]$$ $$6144$$ $$0.61016$$
6720.bv4 6720cc4 $$[0, 1, 0, -1, -5185]$$ $$-8/354375$$ $$-11612160000$$ $$[2]$$ $$6144$$ $$0.61016$$

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form6720.2.a.cc

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.