# Properties

 Label 2730.o Number of curves 8 Conductor 2730 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("2730.o1")
sage: E.isogeny_class()

## Elliptic curves in class 2730.o

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
2730.o1 2730n7 [1, 0, 1, -2265679, -1312610494] 2 82944
2730.o2 2730n8 [1, 0, 1, -996559, 370812482] 2 82944
2730.o3 2730n5 [1, 0, 1, -987844, 377820686] 6 27648
2730.o4 2730n6 [1, 0, 1, -156559, -15923518] 4 41472
2730.o5 2730n4 [1, 0, 1, -68764, 4472462] 6 27648
2730.o6 2730n2 [1, 0, 1, -61744, 5898926] 12 13824
2730.o7 2730n1 [1, 0, 1, -3424, 113582] 6 6912 $$\Gamma_0(N)$$-optimal
2730.o8 2730n3 [1, 0, 1, 27761, -1694014] 2 20736

## Rank

sage: E.rank()

The elliptic curves in class 2730.o have rank $$0$$.

## Modular form2730.2.a.o

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.