# Properties

 Label 3630.g Number of curves $2$ Conductor $3630$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 3630.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3630.g1 3630i2 [1, 0, 1, -1939, -32914] [] 2592
3630.g2 3630i1 [1, 0, 1, -124, 482]  864 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3630.g have rank $$1$$.

## Complex multiplication

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

## Modular form3630.2.a.g

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 