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

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-2100.1-z
• Conductor: 2100.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 2100.1-z over \(\Q(\sqrt{21}) \)

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

Curve label	Weierstrass Coefficients
2100.1-z1	\( \bigl[1\) , \( 1\) , \( 1\) , \( -980\) , \( -15325\bigr] \)
2100.1-z2	\( \bigl[1\) , \( 1\) , \( 1\) , \( 10\) , \( -13\bigr] \)
2100.1-z3	\( \bigl[1\) , \( 1\) , \( 1\) , \( -70\) , \( -205\bigr] \)
2100.1-z4	\( \bigl[1\) , \( 1\) , \( 1\) , \( -370\) , \( 2435\bigr] \)
2100.1-z5	\( \bigl[1\) , \( 1\) , \( 1\) , \( -1050\) , \( -13533\bigr] \)
2100.1-z6	\( \bigl[1\) , \( 1\) , \( 1\) , \( -16800\) , \( -845133\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 8 & 2 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph