# Properties

 Label 151725.cx Number of curves 4 Conductor 151725 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("151725.cx1")

sage: E.isogeny_class()

## Elliptic curves in class 151725.cx

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
151725.cx1 151725cj3 [1, 0, 1, -12181501, 16362653273]  7077888
151725.cx2 151725cj4 [1, 0, 1, -3872751, -2727241727]  7077888
151725.cx3 151725cj2 [1, 0, 1, -802126, 226699523] [2, 2] 3538944
151725.cx4 151725cj1 [1, 0, 1, 100999, 20787023]  1769472 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 151725.cx have rank $$1$$.

## Modular form 151725.2.a.cx

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 