Elliptic curve isogeny class 63.1-b over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-63.1-b
• Conductor: 63.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 63.1-b over \(\Q(\sqrt{21}) \)

Isogeny class 63.1-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
63.1-b1	\( \bigl[a\) , \( -1\) , \( 0\) , \( -102 a - 204\) , \( -2604 a - 4557\bigr] \)
63.1-b2	\( \bigl[a\) , \( -1\) , \( 0\) , \( 3 a + 6\) , \( 0\bigr] \)
63.1-b3	\( \bigl[a\) , \( -1\) , \( 0\) , \( -12 a - 24\) , \( -12 a - 21\bigr] \)
63.1-b4	\( \bigl[a\) , \( -1\) , \( 0\) , \( -117 a - 234\) , \( 1080 a + 1890\bigr] \)
63.1-b5	\( \bigl[a\) , \( -1\) , \( 0\) , \( -147 a - 294\) , \( -1632 a - 2856\bigr] \)
63.1-b6	\( \bigl[a\) , \( -1\) , \( 0\) , \( -2352 a - 4704\) , \( -102180 a - 178815\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph