# Properties

 Label 3630.z Number of curves $2$ Conductor $3630$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("z1")

sage: E.isogeny_class()

## Elliptic curves in class 3630.z

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3630.z1 3630x1 [1, 0, 0, -166680, -26196048] [2] 21120 $$\Gamma_0(N)$$-optimal
3630.z2 3630x2 [1, 0, 0, -140060, -34836900] [2] 42240

## Rank

sage: E.rank()

The elliptic curves in class 3630.z have rank $$0$$.

## Complex multiplication

The elliptic curves in class 3630.z do not have complex multiplication.

## Modular form3630.2.a.z

sage: E.q_eigenform(10)

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

## 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 LMFDB 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 LMFDB labels.