# Properties

 Label 1230k Number of curves 2 Conductor 1230 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1230.k1")
sage: E.isogeny_class()

## Elliptic curves in class 1230k

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
1230.k2 1230k1 [1, 0, 0, 2305, -15975] 7 1960 $$\Gamma_0(N)$$-optimal
1230.k1 1230k2 [1, 0, 0, -1202045, -507358545] 1 13720

## Rank

sage: E.rank()

The elliptic curves in class 1230k have rank $$0$$.

## Modular form1230.2.a.k

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

## 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 Cremona numbering.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 