# Properties

 Label 127050hg Number of curves 4 Conductor 127050 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("127050.hx1")

sage: E.isogeny_class()

## Elliptic curves in class 127050hg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
127050.hx3 127050hg1 [1, 0, 0, -1515588, 623457792]  4423680 $$\Gamma_0(N)$$-optimal
127050.hx2 127050hg2 [1, 0, 0, -6416088, -5634480708] [2, 2] 8847360
127050.hx4 127050hg3 [1, 0, 0, 8557662, -28020236958]  17694720
127050.hx1 127050hg4 [1, 0, 0, -99797838, -383737186458]  17694720

## Rank

sage: E.rank()

The elliptic curves in class 127050hg have rank $$0$$.

## Modular form 127050.2.a.hx

sage: E.q_eigenform(10)

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

## 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 Cremona 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 Cremona labels. 