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, 27320313468836296300]	[2]	7644119040
338130.y3	338130y8	[1, -1, 0, -1069506558180, 428505349689527476]	[2]	7644119040

Rank

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

Complex multiplication

The elliptic curves in class 338130y do not have complex multiplication.

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.