# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("930.c1")

sage: E.isogeny_class()

## Elliptic curves in class 930e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
930.c2 930e1 [1, 1, 0, 3, 9]  96 $$\Gamma_0(N)$$-optimal
930.c1 930e2 [1, 1, 0, -47, 99]  192

## Rank

sage: E.rank()

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

## Modular form930.2.a.c

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. 