# Properties

 Label 2310o Number of curves $6$ Conductor $2310$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("o1")

sage: E.isogeny_class()

## Elliptic curves in class 2310o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2310.o5 2310o1 $$[1, 1, 1, -332850, 86465727]$$ $$-4078208988807294650401/880065599546327040$$ $$-880065599546327040$$ $$[4]$$ $$46080$$ $$2.1643$$ $$\Gamma_0(N)$$-optimal
2310.o4 2310o2 $$[1, 1, 1, -5575730, 5065104575]$$ $$19170300594578891358373921/671785075055001600$$ $$671785075055001600$$ $$[2, 4]$$ $$92160$$ $$2.5109$$
2310.o3 2310o3 $$[1, 1, 1, -5826610, 4584017087]$$ $$21876183941534093095979041/3572502915711058560000$$ $$3572502915711058560000$$ $$[2, 2]$$ $$184320$$ $$2.8574$$
2310.o1 2310o4 $$[1, 1, 1, -89210930, 324283935935]$$ $$78519570041710065450485106721/96428056919040$$ $$96428056919040$$ $$[4]$$ $$184320$$ $$2.8574$$
2310.o2 2310o5 $$[1, 1, 1, -26238610, -47360440513]$$ $$1997773216431678333214187041/187585177195046990066400$$ $$187585177195046990066400$$ $$[2]$$ $$368640$$ $$3.2040$$
2310.o6 2310o6 $$[1, 1, 1, 10571310, 25743893055]$$ $$130650216943167617311657439/361816948816603087500000$$ $$-361816948816603087500000$$ $$[2]$$ $$368640$$ $$3.2040$$

## Rank

sage: E.rank()

The elliptic curves in class 2310o have rank $$0$$.

## Complex multiplication

The elliptic curves in class 2310o do not have complex multiplication.

## Modular form2310.2.a.o

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{7} + q^{8} + q^{9} + q^{10} - q^{11} - q^{12} - 2 q^{13} + q^{14} - q^{15} + q^{16} + 2 q^{17} + q^{18} - 4 q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.