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

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-1764.1-a
• Conductor: 1764.1
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
1764.1-a1	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -8 a + 22\) , \( -387 a + 1064\bigr] \)
1764.1-a2	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 412 a - 1238\) , \( -7107 a + 19544\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph