Elliptic curve isogeny class 25.3-a over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-25.3-a
• Conductor: 25.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 25.3-a over \(\Q(\sqrt{21}) \)

Isogeny class 25.3-a contains 4 curves linked by isogenies of degrees dividing 14.

Curve label	Weierstrass Coefficients
25.3-a1	\( \bigl[1\) , \( -1\) , \( a\) , \( 2 a - 7\) , \( -5 a + 12\bigr] \)
25.3-a2	\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -a - 3\) , \( -1\bigr] \)
25.3-a3	\( \bigl[1\) , \( -1\) , \( a\) , \( 42 a - 122\) , \( -246 a + 683\bigr] \)
25.3-a4	\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -16 a - 38\) , \( 43 a + 66\bigr] \)

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