Elliptic curve isogeny class 1764.1-n over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-1764.1-n
• Conductor: 1764.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 1764.1-n over \(\Q(\sqrt{21}) \)

Isogeny class 1764.1-n contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
1764.1-n1	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 2134 a - 6404\) , \( 88821 a - 244258\bigr] \)
1764.1-n2	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -71 a + 211\) , \( 621 a - 1708\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph