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

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

Isogeny class 2100.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
2100.1-a1	\( \bigl[a\) , \( -a\) , \( 1\) , \( -a + 3\) , \( 77 a + 140\bigr] \)
2100.1-a2	\( \bigl[a\) , \( -a\) , \( 1\) , \( -11 a - 17\) , \( 29 a + 52\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph