Elliptic curve isogeny class 100.1-c over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-100.1-c
• Number of curves: 4
• Conductor: 100.1
• Rank: \( 1 \)

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

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

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

Elliptic curves in class 100.1-c over \(\Q(\sqrt{21}) \)

Isogeny class 100.1-c contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
100.1-c1	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 2 a - 8\) , \( 5 a - 14\bigr] \)
100.1-c2	\( \bigl[a\) , \( -1\) , \( 0\) , \( 2 a + 4\) , \( 0\bigr] \)
100.1-c3	\( \bigl[a\) , \( -1\) , \( 0\) , \( -8 a - 16\) , \( -8 a - 14\bigr] \)
100.1-c4	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 42 a - 128\) , \( 261 a - 718\bigr] \)