Elliptic curve isogeny class 847.1-a over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-847.1-a
• Conductor: 847.1
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 847.1-a over \(\Q(\sqrt{21}) \)

Isogeny class 847.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
847.1-a1	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 18 a + 34\) , \( -195 a - 351\bigr] \)
847.1-a2	\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 260 a - 717\) , \( 3155 a - 8805\bigr] \)