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

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-768.1-q
• Conductor: 768.1
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
768.1-q1	\( \bigl[0\) , \( 1\) , \( 0\) , \( 16\) , \( 180\bigr] \)
768.1-q2	\( \bigl[0\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
768.1-q3	\( \bigl[0\) , \( 1\) , \( 0\) , \( -4\) , \( -4\bigr] \)
768.1-q4	\( \bigl[0\) , \( 1\) , \( 0\) , \( -24\) , \( 36\bigr] \)
768.1-q5	\( \bigl[0\) , \( 1\) , \( 0\) , \( -64\) , \( -220\bigr] \)
768.1-q6	\( \bigl[0\) , \( 1\) , \( 0\) , \( -384\) , \( 2772\bigr] \)

Rank

Rank: \( 1 \)

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