# Properties

 Label 6720.ci Number of curves $4$ Conductor $6720$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("ci1")

sage: E.isogeny_class()

## Elliptic curves in class 6720.ci

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6720.ci1 6720cm3 $$[0, 1, 0, -262305, 51618303]$$ $$60910917333827912/3255076125$$ $$106662334464000$$ $$$$ $$36864$$ $$1.7591$$
6720.ci2 6720cm2 $$[0, 1, 0, -17305, 707303]$$ $$139927692143296/27348890625$$ $$112021056000000$$ $$[2, 2]$$ $$18432$$ $$1.4126$$
6720.ci3 6720cm1 $$[0, 1, 0, -5300, -140250]$$ $$257307998572864/19456203375$$ $$1245197016000$$ $$$$ $$9216$$ $$1.0660$$ $$\Gamma_0(N)$$-optimal
6720.ci4 6720cm4 $$[0, 1, 0, 35615, 4231775]$$ $$152461584507448/322998046875$$ $$-10584000000000000$$ $$$$ $$36864$$ $$1.7591$$

## Rank

sage: E.rank()

The elliptic curves in class 6720.ci have rank $$1$$.

## Complex multiplication

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

## Modular form6720.2.a.ci

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 