# Properties

 Label 930g Number of curves $4$ Conductor $930$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("930.g1")

sage: E.isogeny_class()

## Elliptic curves in class 930g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
930.g3 930g1 [1, 0, 1, -244, 1442]  288 $$\Gamma_0(N)$$-optimal
930.g2 930g2 [1, 0, 1, -264, 1186] [2, 2] 576
930.g1 930g3 [1, 0, 1, -1514, -21814]  1152
930.g4 930g4 [1, 0, 1, 666, 7882]  1152

## Rank

sage: E.rank()

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

## Modular form930.2.a.g

sage: E.q_eigenform(10)

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

## 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. 