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

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

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

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

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

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

Curve label	Weierstrass Coefficients
192.1-k1	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
192.1-k2	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 20 a - 64\) , \( -108 a + 300\bigr] \)
192.1-k3	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -4\) , \( -4 a + 4\bigr] \)
192.1-k4	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -20 a - 24\) , \( -76 a - 116\bigr] \)

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