# Properties

 Label 364650.ci Number of curves $4$ Conductor $364650$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 364650.ci

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
364650.ci1 364650ci4 $$[1, 0, 1, -62741328601, -6048934264659652]$$ $$1748094148784980747354970849498497/887694600425282263291392$$ $$13870228131645035363928000000$$ $$[2]$$ $$1210318848$$ $$4.7327$$
364650.ci2 364650ci3 $$[1, 0, 1, -8582608601, 168305381804348]$$ $$4474676144192042711273397261697/1806328356954994499451382272$$ $$28223880577421789053927848000000$$ $$[2]$$ $$1210318848$$ $$4.7327$$
364650.ci3 364650ci2 $$[1, 0, 1, -3942544601, -93440628435652]$$ $$433744050935826360922067531137/9612122270219882316693504$$ $$150189410472185661198336000000$$ $$[2, 2]$$ $$605159424$$ $$4.3861$$
364650.ci4 364650ci1 $$[1, 0, 1, 22383399, -4475573971652]$$ $$79374649975090937760383/553856914190911653543936$$ $$-8654014284232994586624000000$$ $$[2]$$ $$302579712$$ $$4.0396$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 364650.ci have rank $$0$$.

## Complex multiplication

The elliptic curves in class 364650.ci do not have complex multiplication.

## Modular form 364650.2.a.ci

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} + q^{11} + q^{12} - q^{13} + q^{16} + q^{17} - q^{18} + 8q^{19} + O(q^{20})$$

## 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.