Elliptic curve isogeny class 256.1-d over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-256.1-d
• Conductor: 256.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 256.1-d over \(\Q(\sqrt{21}) \)

Isogeny class 256.1-d contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
256.1-d1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 2\) , \( 0\bigr] \)
256.1-d2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 2\) , \( 2\bigr] \)
256.1-d3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -4 a - 8\) , \( 16 a + 28\bigr] \)
256.1-d4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 6 a - 13\) , \( -11 a + 31\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph