Properties

 Label 127050hy Number of curves $6$ Conductor $127050$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("127050.is1")

sage: E.isogeny_class()

Elliptic curves in class 127050hy

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
127050.is6 127050hy1 [1, 0, 0, 30187, 2827617] [2] 983040 $$\Gamma_0(N)$$-optimal
127050.is5 127050hy2 [1, 0, 0, -211813, 29205617] [2, 2] 1966080
127050.is4 127050hy3 [1, 0, 0, -1119313, -430896883] [2] 3932160
127050.is2 127050hy4 [1, 0, 0, -3176313, 2178468117] [2, 2] 3932160
127050.is3 127050hy5 [1, 0, 0, -2964563, 2481482367] [2] 7864320
127050.is1 127050hy6 [1, 0, 0, -50820063, 139440111867] [2] 7864320

Rank

sage: E.rank()

The elliptic curves in class 127050hy have rank $$1$$.

Modular form 127050.2.a.is

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.