# Properties

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

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

sage: E.isogeny_class()

## Elliptic curves in class 930g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
930.g3 930g1 $$[1, 0, 1, -244, 1442]$$ $$1597099875769/186000$$ $$186000$$ $$$$ $$288$$ $$0.037436$$ $$\Gamma_0(N)$$-optimal
930.g2 930g2 $$[1, 0, 1, -264, 1186]$$ $$2023804595449/540562500$$ $$540562500$$ $$[2, 2]$$ $$576$$ $$0.38401$$
930.g1 930g3 $$[1, 0, 1, -1514, -21814]$$ $$383432500775449/18701300250$$ $$18701300250$$ $$$$ $$1152$$ $$0.73058$$
930.g4 930g4 $$[1, 0, 1, 666, 7882]$$ $$32740359775271/45410156250$$ $$-45410156250$$ $$$$ $$1152$$ $$0.73058$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## 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. 