Elliptic curve isogeny class 192.1-f over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-192.1-f
• Conductor: 192.1
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 192.1-f over \(\Q(\sqrt{21}) \)

Isogeny class 192.1-f contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
192.1-f1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 20 a - 44\) , \( 76 a - 192\bigr] \)
192.1-f2	\( \bigl[0\) , \( -a\) , \( 0\) , \( 1\) , \( 0\bigr] \)
192.1-f3	\( \bigl[0\) , \( -a\) , \( 0\) , \( -4\) , \( 4 a\bigr] \)
192.1-f4	\( \bigl[0\) , \( -a\) , \( 0\) , \( -20 a - 44\) , \( 108 a + 192\bigr] \)