# Properties

 Label 222530n Number of curves 4 Conductor 222530 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("222530.bw1")

sage: E.isogeny_class()

## Elliptic curves in class 222530n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
222530.bw3 222530n1 [1, 1, 1, -16190, 15423355] [2] 2985984 $$\Gamma_0(N)$$-optimal
222530.bw2 222530n2 [1, 1, 1, -1033470, 400362107] [2] 5971968
222530.bw4 222530n3 [1, 1, 1, 145650, -415588933] [2] 8957952
222530.bw1 222530n4 [1, 1, 1, -7547530, -7757959925] [2] 17915904

## Rank

sage: E.rank()

The elliptic curves in class 222530n have rank $$0$$.

## Modular form 222530.2.a.bw

sage: E.q_eigenform(10)

$$q + q^{2} + 2q^{3} + q^{4} + q^{5} + 2q^{6} - q^{7} + q^{8} + q^{9} + q^{10} + q^{11} + 2q^{12} - 4q^{13} - q^{14} + 2q^{15} + q^{16} + q^{18} - 4q^{19} + O(q^{20})$$

## 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.