Elliptic curve isogeny class 324.1-c over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-324.1-c
• Conductor: 324.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 324.1-c over \(\Q(\sqrt{21}) \)

Isogeny class 324.1-c contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
324.1-c1	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 9 a - 30\) , \( -27 a + 70\bigr] \)
324.1-c2	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 4 a - 14\) , \( 13 a - 36\bigr] \)
324.1-c3	\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 2 a + 8\) , \( -6 a - 8\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph