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

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-847.1-c
• Conductor: 847.1
• Rank: \( 0 \)

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

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

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

Isogeny class 847.1-c contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
847.1-c1	\( \bigl[0\) , \( 1\) , \( 1\) , \( -89\) , \( 295\bigr] \)
847.1-c2	\( \bigl[0\) , \( 1\) , \( 1\) , \( -49\) , \( 600\bigr] \)
847.1-c3	\( \bigl[0\) , \( 1\) , \( 1\) , \( 441\) , \( -15815\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph