Elliptic curve isogeny class 2268.1-d over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-2268.1-d
• Conductor: 2268.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 2268.1-d over \(\Q(\sqrt{21}) \)

Isogeny class 2268.1-d contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
2268.1-d1	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -159 a + 426\) , \( -1113 a + 3122\bigr] \)
2268.1-d2	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 6 a - 24\) , \( 24 a - 96\bigr] \)
2268.1-d3	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 21 a - 54\) , \( 99 a - 274\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph