Elliptic Curve Isogeny Class with Cremona label 33150b (LMFDB label 33150.l)

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

Elliptic curves in class 33150b

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

The elliptic curves in class 33150b have rank \(1\).

Modular form 33150.2.a.l

Isogeny 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

The vertices are labelled with Cremona labels.