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

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-768.1-bj
• 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-bj over \(\Q(\sqrt{21}) \)

Isogeny class 768.1-bj contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
768.1-bj1	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 4 a - 10\) , \( 11 a - 31\bigr] \)
768.1-bj2	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 9 a - 25\) , \( -5 a + 14\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph