# Properties

 Label 3630.n Number of curves $4$ Conductor $3630$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 3630.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3630.n1 3630n3 [1, 1, 1, -503786, -105462367]  76800
3630.n2 3630n2 [1, 1, 1, -171036, 25774233] [2, 2] 38400
3630.n3 3630n1 [1, 1, 1, -168616, 26579609]  19200 $$\Gamma_0(N)$$-optimal
3630.n4 3630n4 [1, 1, 1, 122994, 105515169]  76800

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form3630.2.a.n

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 