Elliptic curve isogeny class 252.1-d over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-252.1-d
• Conductor: 252.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 252.1-d over \(\Q(\sqrt{21}) \)

Isogeny class 252.1-d contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
252.1-d1	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 511 a - 1535\) , \( 10485 a - 28834\bigr] \)
252.1-d2	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( a - 5\) , \( -3 a + 8\bigr] \)
252.1-d3	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -14 a + 40\) , \( 69 a - 190\bigr] \)
252.1-d4	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 106 a - 320\) , \( 837 a - 2302\bigr] \)
252.1-d5	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 31 a - 95\) , \( -147 a + 404\bigr] \)
252.1-d6	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 8191 a - 24575\) , \( 661749 a - 1819810\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph