# Properties

 Label 3675.n Number of curves 6 Conductor 3675 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("3675.n1")
sage: E.isogeny_class()

## Elliptic curves in class 3675.n

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
3675.n1 3675j5 [1, 0, 1, -960426, 362199373] 2 24576
3675.n2 3675j4 [1, 0, 1, -60051, 5650873] 4 12288
3675.n3 3675j3 [1, 0, 1, -47801, -4002127] 2 12288
3675.n4 3675j6 [1, 0, 1, -41676, 9178873] 2 24576
3675.n5 3675j2 [1, 0, 1, -4926, 28123] 4 6144
3675.n6 3675j1 [1, 0, 1, 1199, 3623] 2 3072 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3675.n have rank $$1$$.

## Modular form3675.2.a.n

sage: E.q_eigenform(10)
$$q + q^{2} + q^{3} - q^{4} + q^{6} - 3q^{8} + q^{9} + 4q^{11} - q^{12} - 2q^{13} - q^{16} - 6q^{17} + q^{18} - 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 8 & 4 & 4 & 8 \\ 2 & 1 & 4 & 2 & 2 & 4 \\ 8 & 4 & 1 & 8 & 2 & 4 \\ 4 & 2 & 8 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.