Elliptic curve isogeny class 192.6-g over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-192.6-g
• Conductor: 192.6
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 192.6-g over \(\Q(\sqrt{57}) \)

Isogeny class 192.6-g contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
192.6-g1	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 6 a + 30\) , \( 13 a + 49\bigr] \)
192.6-g2	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 10 a - 31\) , \( -23 a + 106\bigr] \)
192.6-g3	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 135 a - 566\) , \( -1618 a + 6923\bigr] \)
192.6-g4	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 4129 a - 17623\) , \( 203103 a - 868203\bigr] \)