# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("j1")

sage: E.isogeny_class()

## Elliptic curves in class 930.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
930.j1 930j2 $$[1, 0, 1, -218448, 39279646]$$ $$1152829477932246539641/3188367360$$ $$3188367360$$ $$$$ $$4160$$ $$1.4817$$
930.j2 930j1 $$[1, 0, 1, -13648, 613406]$$ $$-281115640967896441/468084326400$$ $$-468084326400$$ $$$$ $$2080$$ $$1.1351$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form930.2.a.j

sage: E.q_eigenform(10)

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