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

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

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

Curve label	Weierstrass Coefficients
2100.1-i1	\( \bigl[1\) , \( a - 1\) , \( 0\) , \( -41 a - 99\) , \( 2045 a + 3630\bigr] \)
2100.1-i2	\( \bigl[1\) , \( a - 1\) , \( 0\) , \( -11 a - 19\) , \( -13 a - 22\bigr] \)
2100.1-i3	\( \bigl[1\) , \( a - 1\) , \( 0\) , \( -111 a - 199\) , \( 887 a + 1590\bigr] \)
2100.1-i4	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -1053 a + 2926\) , \( 5109 a - 14250\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph