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

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-25.2-b
• Conductor: 25.2
• Rank: \( 1 \)

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

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

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

Isogeny class 25.2-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
25.2-b1	\( \bigl[0\) , \( a + 1\) , \( a + 1\) , \( a + 2\) , \( -2 a + 4\bigr] \)
25.2-b2	\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( a + 2\) , \( -a - 2\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph