# Properties

 Label 2310.i Number of curves $4$ Conductor $2310$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("i1")

sage: E.isogeny_class()

## Elliptic curves in class 2310.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2310.i1 2310i3 $$[1, 0, 1, -9314, -342988]$$ $$89343998142858649/1112702976000$$ $$1112702976000$$ $$$$ $$5184$$ $$1.1212$$
2310.i2 2310i4 $$[1, 0, 1, -1634, -889804]$$ $$-482056280171929/341652696000000$$ $$-341652696000000$$ $$$$ $$10368$$ $$1.4678$$
2310.i3 2310i1 $$[1, 0, 1, -899, 10046]$$ $$80224711835689/2173469760$$ $$2173469760$$ $$$$ $$1728$$ $$0.57191$$ $$\Gamma_0(N)$$-optimal
2310.i4 2310i2 $$[1, 0, 1, 181, 32942]$$ $$661003929431/468755040600$$ $$-468755040600$$ $$$$ $$3456$$ $$0.91848$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form2310.2.a.i

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 