# Properties

 Label 2310.l Number of curves 8 Conductor 2310 CM no Rank 0 Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("2310.l1")
sage: E.isogeny_class()

## Elliptic curves in class 2310.l

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
2310.l1 2310l7 [1, 0, 1, -256428, 46871746] 2 27648
2310.l2 2310l4 [1, 0, 1, -252003, 48670756] 6 9216
2310.l3 2310l6 [1, 0, 1, -50628, -3508094] 4 13824
2310.l4 2310l3 [1, 0, 1, -47748, -4019582] 2 6912
2310.l5 2310l2 [1, 0, 1, -15753, 759256] 12 4608
2310.l6 2310l5 [1, 0, 1, -12783, 1055068] 6 9216
2310.l7 2310l1 [1, 0, 1, -1173, 6928] 6 2304 $$\Gamma_0(N)$$-optimal
2310.l8 2310l8 [1, 0, 1, 109092, -21141182] 2 27648

## Rank

sage: E.rank()

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

## Modular form2310.2.a.l

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

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 4 & 6 & 12 & 12 & 4 \\ 3 & 1 & 6 & 12 & 2 & 4 & 4 & 12 \\ 2 & 6 & 1 & 2 & 3 & 6 & 6 & 2 \\ 4 & 12 & 2 & 1 & 6 & 12 & 3 & 4 \\ 6 & 2 & 3 & 6 & 1 & 2 & 2 & 6 \\ 12 & 4 & 6 & 12 & 2 & 1 & 4 & 3 \\ 12 & 4 & 6 & 3 & 2 & 4 & 1 & 12 \\ 4 & 12 & 2 & 4 & 6 & 3 & 12 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.