Properties

 Label 33150b Number of curves 8 Conductor 33150 CM no Rank 1 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("33150.l1")

sage: E.isogeny_class()

Elliptic curves in class 33150b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33150.l7 33150b1 [1, 1, 0, -52403650, 140576384500] [2] 6635520 $$\Gamma_0(N)$$-optimal
33150.l6 33150b2 [1, 1, 0, -138931650, -443401087500] [2, 2] 13271040
33150.l5 33150b3 [1, 1, 0, -644819650, -6261614367500] [2] 19906560
33150.l8 33150b4 [1, 1, 0, 372020350, -2946554935500] [2] 26542080
33150.l4 33150b5 [1, 1, 0, -2034331650, -35313074887500] [2] 26542080
33150.l2 33150b6 [1, 1, 0, -10298437650, -402262678345500] [2, 2] 39813120
33150.l3 33150b7 [1, 1, 0, -10279763150, -403794192765000] [2] 79626240
33150.l1 33150b8 [1, 1, 0, -164775000150, -25744606186158000] [2] 79626240

Rank

sage: E.rank()

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

Modular form 33150.2.a.l

sage: E.q_eigenform(10)

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

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.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with Cremona labels.