# Properties

 Label 930n Number of curves $4$ Conductor $930$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("930.n1")

sage: E.isogeny_class()

## Elliptic curves in class 930n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
930.n4 930n1 [1, 0, 0, 1389, -22239] [6] 1440 $$\Gamma_0(N)$$-optimal
930.n3 930n2 [1, 0, 0, -8531, -218655] [6] 2880
930.n2 930n3 [1, 0, 0, -39651, -3060495] [2] 4320
930.n1 930n4 [1, 0, 0, -635471, -195033699] [2] 8640

## Rank

sage: E.rank()

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

## Modular form930.2.a.n

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + 2q^{7} + q^{8} + q^{9} - q^{10} + q^{12} - 4q^{13} + 2q^{14} - q^{15} + q^{16} + 6q^{17} + q^{18} + 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels.