Elliptic curve isogeny class 192.7-b over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-192.7-b
• Conductor: 192.7
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 192.7-b over \(\Q(\sqrt{57}) \)

Isogeny class 192.7-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
192.7-b1	\( \bigl[a\) , \( -a\) , \( a\) , \( 1166 a + 3825\) , \( 2865484 a + 9384228\bigr] \)
192.7-b2	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 53 a - 206\) , \( -400 a + 1728\bigr] \)
192.7-b3	\( \bigl[a\) , \( 1\) , \( a\) , \( -7 a - 24\) , \( -25 a - 83\bigr] \)
192.7-b4	\( \bigl[a\) , \( -a\) , \( a\) , \( -9219 a - 30185\) , \( 915566 a + 2998408\bigr] \)
192.7-b5	\( \bigl[a\) , \( 1\) , \( a\) , \( -102 a - 334\) , \( -1281 a - 4195\bigr] \)
192.7-b6	\( \bigl[a\) , \( 1\) , \( a\) , \( 288 a - 1230\) , \( 13767 a - 58851\bigr] \)