Elliptic curve isogeny class 768.1-bi over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-768.1-bi
• Conductor: 768.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{21}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 5 \); class number \(1\).

Elliptic curves in class 768.1-bi over \(\Q(\sqrt{21}) \)

Isogeny class 768.1-bi contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
768.1-bi1	\( \bigl[0\) , \( a\) , \( 0\) , \( -78 a + 221\) , \( 4241 a - 11838\bigr] \)
768.1-bi2	\( \bigl[0\) , \( a\) , \( 0\) , \( -3 a + 11\) , \( -4 a + 12\bigr] \)
768.1-bi3	\( \bigl[0\) , \( a\) , \( 0\) , \( 22 a - 59\) , \( -75 a + 210\bigr] \)
768.1-bi4	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -122 a - 217\) , \( -985 a - 1765\bigr] \)
768.1-bi5	\( \bigl[0\) , \( a\) , \( 0\) , \( 322 a - 899\) , \( -4959 a + 13842\bigr] \)
768.1-bi6	\( \bigl[0\) , \( a\) , \( 0\) , \( 1922 a - 5379\) , \( 68449 a - 191102\bigr] \)

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