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

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-2268.1-k
• Conductor: 2268.1
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
2268.1-k1	\( \bigl[a\) , \( -1\) , \( 0\) , \( -354 a - 708\) , \( -6040 a - 10570\bigr] \)
2268.1-k2	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 36 a - 111\) , \( -252 a + 682\bigr] \)
2268.1-k3	\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 29 a + 62\) , \( 93 a + 172\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph