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

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

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

Curve label	Weierstrass Coefficients
2100.1-h1	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 6 a - 3\) , \( 55 a + 131\bigr] \)
2100.1-h2	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 626 a - 3203\) , \( -26113 a + 61171\bigr] \)
2100.1-h3	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -74 a - 403\) , \( 1047 a + 3491\bigr] \)
2100.1-h4	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -2054 a - 4003\) , \( 83055 a + 149651\bigr] \)

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