Elliptic curve isogeny class 25.2-a over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-25.2-a
• Conductor: 25.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 25.2-a over \(\Q(\sqrt{21}) \)

Isogeny class 25.2-a contains 4 curves linked by isogenies of degrees dividing 14.

Curve label	Weierstrass Coefficients
25.2-a1	\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -a - 3\) , \( -a - 1\bigr] \)
25.2-a2	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -3 a - 5\) , \( 4 a + 7\bigr] \)
25.2-a3	\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 14 a - 53\) , \( -44 a + 109\bigr] \)
25.2-a4	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -43 a - 80\) , \( 245 a + 437\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 7 & 2 & 14 \\ 7 & 1 & 14 & 2 \\ 2 & 14 & 1 & 7 \\ 14 & 2 & 7 & 1 \end{array}\right)\)

Isogeny graph