# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("2310.i1")

sage: E.isogeny_class()

## Elliptic curves in class 2310.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2310.i1 2310i3 [1, 0, 1, -9314, -342988]  5184
2310.i2 2310i4 [1, 0, 1, -1634, -889804]  10368
2310.i3 2310i1 [1, 0, 1, -899, 10046]  1728 $$\Gamma_0(N)$$-optimal
2310.i4 2310i2 [1, 0, 1, 181, 32942]  3456

## Rank

sage: E.rank()

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

## Modular form2310.2.a.i

sage: E.q_eigenform(10)

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

## 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 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. 