# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("2310.m1")

sage: E.isogeny_class()

## Elliptic curves in class 2310m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2310.m3 2310m1 [1, 1, 1, -501, -3957]  1536 $$\Gamma_0(N)$$-optimal
2310.m2 2310m2 [1, 1, 1, -2121, 32979] [2, 2] 3072
2310.m1 2310m3 [1, 1, 1, -32991, 2292663]  6144
2310.m4 2310m4 [1, 1, 1, 2829, 169599]  6144

## Rank

sage: E.rank()

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

## Modular form2310.2.a.m

sage: E.q_eigenform(10)

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

## 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 Cremona 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 Cremona labels. 