Elliptic curve isogeny class 576.1-k over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-576.1-k
• Conductor: 576.1
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 576.1-k over \(\Q(\sqrt{21}) \)

Isogeny class 576.1-k contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
576.1-k1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 48 a + 96\) , \( -2160 a - 3780\bigr] \)
576.1-k2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 3 a + 6\) , \( 0\bigr] \)
576.1-k3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -12 a - 24\) , \( 48 a + 84\bigr] \)
576.1-k4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -72 a - 144\) , \( -432 a - 756\bigr] \)
576.1-k5	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -192 a - 384\) , \( 2640 a + 4620\bigr] \)
576.1-k6	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -1152 a - 2304\) , \( -33264 a - 58212\bigr] \)