# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

## Elliptic curves in class 930e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
930.c2 930e1 $$[1, 1, 0, 3, 9]$$ $$1685159/27900$$ $$-27900$$ $$$$ $$96$$ $$-0.46643$$ $$\Gamma_0(N)$$-optimal
930.c1 930e2 $$[1, 1, 0, -47, 99]$$ $$11867954041/778410$$ $$778410$$ $$$$ $$192$$ $$-0.11985$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form930.2.a.e

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 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.
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