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

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

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

Curve label	Weierstrass Coefficients
2100.1-k1	\( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( 350 a + 729\) , \( -18319 a - 33077\bigr] \)
2100.1-k2	\( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( -290 a - 551\) , \( -3983 a - 7221\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph