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

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-576.1-c
• 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-c over \(\Q(\sqrt{21}) \)

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

Curve label	Weierstrass Coefficients
576.1-c1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -46 a + 143\) , \( 2113 a - 5797\bigr] \)
576.1-c2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -a + 8\) , \( -2 a + 8\bigr] \)
576.1-c3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 14 a - 37\) , \( -35 a + 95\bigr] \)
576.1-c4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 74 a - 217\) , \( 505 a - 1405\bigr] \)
576.1-c5	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 194 a - 577\) , \( -2447 a + 6683\bigr] \)
576.1-c6	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 1154 a - 3457\) , \( 34417 a - 94933\bigr] \)