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

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

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

Curve label	Weierstrass Coefficients
2100.1-c1	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -15 a + 15\) , \( -3033 a - 4365\bigr] \)
2100.1-c2	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 5 a + 5\) , \( 5 a + 17\bigr] \)
2100.1-c3	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 5 a - 75\) , \( -75 a + 225\bigr] \)
2100.1-c4	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -95 a - 255\) , \( -1215 a - 1823\bigr] \)
2100.1-c5	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 105 a - 1175\) , \( -2455 a + 15905\bigr] \)
2100.1-c6	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -1775 a - 3405\) , \( -66357 a - 119633\bigr] \)

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