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

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-100.1-e
• Conductor: 100.1
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
100.1-e1	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 3 a - 5\) , \( -3 a + 7\bigr] \)
100.1-e2	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -925 a - 1665\) , \( -18963 a - 33983\bigr] \)
100.1-e3	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 13 a - 35\) , \( 33 a - 95\bigr] \)
100.1-e4	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 63 a - 180\) , \( 406 a - 1153\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph