Elliptic Curve Isogeny Class with Cremona label 338130y (LMFDB label 338130.y)

• Label: 338130y
• Number of curves: 8
• Conductor: 338130
• CM: no
• Rank: 1

Elliptic curves in class 338130y

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
338130.y7	338130y1	[1, -1, 0, -5452075800, -149202592145600]	[2]	637009920	\(\Gamma_0(N)\)-optimal
338130.y6	338130y2	[1, -1, 0, -14454448920, 470482963468096]	[2, 2]	1274019840
338130.y5	338130y3	[1, -1, 0, -67087036440, 6644606911560256]	[2]	1911029760
338130.y4	338130y4	[1, -1, 0, -211651864920, 37473670967754496]	[2]	2548039680
338130.y8	338130y5	[1, -1, 0, 38704997160, 3127062489980800]	[2]	2548039680
338130.y2	338130y6	[1, -1, 0, -1071449453160, 426880086563858800]	[2, 2]	3822059520
338130.y1	338130y7	[1, -1, 0, -17143191015660, 27320313468836296300L]	[2]	7644119040
338130.y3	338130y8	[1, -1, 0, -1069506558180, 428505349689527476]	[2]	7644119040

Rank

The elliptic curves in class 338130y have rank \(1\).

Modular form 338130.2.a.y

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.