Elliptic curve isogeny class 81.1-a over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-81.1-a
• Conductor: 81.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 81.1-a over \(\Q(\sqrt{21}) \)

Isogeny class 81.1-a contains 4 curves linked by isogenies of degrees dividing 27.

Curve label	Weierstrass Coefficients
81.1-a1	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 11 a - 28\) , \( 31 a - 85\bigr] \)
81.1-a2	\( \bigl[0\) , \( a + 1\) , \( 1\) , \( -9 a - 18\) , \( -41 a - 72\bigr] \)
81.1-a3	\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 3 a + 5\bigr] \)
81.1-a4	\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( -3 a + 8\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 27 & 3 & 9 \\ 27 & 1 & 9 & 3 \\ 3 & 9 & 1 & 3 \\ 9 & 3 & 3 & 1 \end{array}\right)\)

Isogeny graph