# Properties

 Label 930.k Number of curves $2$ Conductor $930$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("k1")

sage: E.isogeny_class()

## Elliptic curves in class 930.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
930.k1 930k2 $$[1, 1, 1, -661, -6817]$$ $$31942518433489/27900$$ $$27900$$ $$$$ $$320$$ $$0.15343$$
930.k2 930k1 $$[1, 1, 1, -41, -121]$$ $$-7633736209/230640$$ $$-230640$$ $$$$ $$160$$ $$-0.19315$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 930.k have rank $$0$$.

## Complex multiplication

The elliptic curves in class 930.k do not have complex multiplication.

## Modular form930.2.a.k

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 