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

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-2100.1-f
• 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-f over \(\Q(\sqrt{21}) \)

Isogeny class 2100.1-f contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
2100.1-f1	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( -12 a + 19\) , \( -10 a - 34\bigr] \)
2100.1-f2	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 153 a - 281\) , \( -1078 a + 3776\bigr] \)
2100.1-f3	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 113 a - 361\) , \( -1206 a + 3392\bigr] \)
2100.1-f4	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( -2 a - 11\) , \( -14 a - 18\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph