# Properties

 Label 930d Number of curves $2$ Conductor $930$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

## Elliptic curves in class 930d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
930.d2 930d1 $$[1, 1, 0, 2238, 181236]$$ $$1238798620042199/14760960000000$$ $$-14760960000000$$ $$$$ $$2688$$ $$1.2078$$ $$\Gamma_0(N)$$-optimal
930.d1 930d2 $$[1, 1, 0, -37442, 2585844]$$ $$5805223604235668521/435937500000000$$ $$435937500000000$$ $$$$ $$5376$$ $$1.5544$$

## Rank

sage: E.rank()

The elliptic curves in class 930d have rank $$1$$.

## Complex multiplication

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

## Modular form930.2.a.d

sage: E.q_eigenform(10)

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