Elliptic curve isogeny class 256.1-g over number field \(\Q(\sqrt{33}) \)

• Base field: \(\Q(\sqrt{33}) \)
• Label: 2.2.33.1-256.1-g
• Conductor: 256.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{33}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 8 \); class number \(1\).

Elliptic curves in class 256.1-g over \(\Q(\sqrt{33}) \)

Isogeny class 256.1-g contains 6 curves linked by isogenies of degrees dividing 99.

Curve label	Weierstrass Coefficients
256.1-g1	\( \bigl[0\) , \( a\) , \( 0\) , \( -6965 a - 16520\) , \( 528427 a + 1253576\bigr] \)
256.1-g2	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -395 a + 1315\) , \( -3275 a + 11027\bigr] \)
256.1-g3	\( \bigl[0\) , \( a\) , \( 0\) , \( -85 a - 200\) , \( 651 a + 1544\bigr] \)
256.1-g4	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 85 a - 285\) , \( -651 a + 2195\bigr] \)
256.1-g5	\( \bigl[0\) , \( a\) , \( 0\) , \( 395 a + 920\) , \( 3275 a + 7752\bigr] \)
256.1-g6	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 6965 a - 23485\) , \( -528427 a + 1782003\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 99 & 3 & 33 & 9 & 11 \\ 99 & 1 & 33 & 3 & 11 & 9 \\ 3 & 33 & 1 & 11 & 3 & 33 \\ 33 & 3 & 11 & 1 & 33 & 3 \\ 9 & 11 & 3 & 33 & 1 & 99 \\ 11 & 9 & 33 & 3 & 99 & 1 \end{array}\right)\)

Isogeny graph