Elliptic curve isogeny class 2100.1-r over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-2100.1-r
• Conductor: 2100.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 2100.1-r over \(\Q(\sqrt{21}) \)

Isogeny class 2100.1-r contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
2100.1-r1	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 4902 a - 13716\) , \( -357994 a + 999325\bigr] \)
2100.1-r2	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 50 a + 92\) , \( 498 a + 891\bigr] \)
2100.1-r3	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 352 a - 976\) , \( -4214 a + 11765\bigr] \)
2100.1-r4	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 1852 a - 5176\) , \( 62146 a - 173515\bigr] \)
2100.1-r5	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 5252 a - 14696\) , \( -314286 a + 877301\bigr] \)
2100.1-r6	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 84002 a - 235196\) , \( -20115186 a + 56153501\bigr] \)

Rank

Rank: \( 1 \)

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