Elliptic curve isogeny class 128.6-j over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-128.6-j
• Conductor: 128.6
• Rank: \( 1 \)

Base field \(\Q(\sqrt{57}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 14 \); class number \(1\).

Elliptic curves in class 128.6-j over \(\Q(\sqrt{57}) \)

Isogeny class 128.6-j contains 4 curves linked by isogenies of degrees dividing 21.

Curve label	Weierstrass Coefficients
128.6-j1	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -1044502 a - 3420890\) , \( 1124767860 a + 3683520340\bigr] \)
128.6-j2	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 25303280 a - 108169436\) , \( 134641581530 a - 575581615086\bigr] \)
128.6-j3	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -382 a - 1250\) , \( 10156 a + 33260\bigr] \)
128.6-j4	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 9410 a - 40226\) , \( 1409836 a - 6026932\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 7 & 21 \\ 3 & 1 & 21 & 7 \\ 7 & 21 & 1 & 3 \\ 21 & 7 & 3 & 1 \end{array}\right)\)

Isogeny graph