# Properties

 Label 33150.n Number of curves 4 Conductor 33150 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("33150.n1")

sage: E.isogeny_class()

## Elliptic curves in class 33150.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33150.n1 33150q4 [1, 0, 1, -1915501, 1018505648]  1105920
33150.n2 33150q3 [1, 0, 1, -1605501, -779074352]  1105920
33150.n3 33150q2 [1, 0, 1, -160501, 4115648] [2, 2] 552960
33150.n4 33150q1 [1, 0, 1, 39499, 515648]  276480 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 33150.n have rank $$1$$.

## Modular form 33150.2.a.n

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{6} - 4q^{7} - q^{8} + q^{9} - 4q^{11} + q^{12} - q^{13} + 4q^{14} + q^{16} + q^{17} - q^{18} + 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 