Elliptic curve isogeny class 900.2-k over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-900.2-k
• Conductor: 900.2
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 900.2-k over \(\Q(\sqrt{21}) \)

Isogeny class 900.2-k contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
900.2-k1	\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -10 a - 13\) , \( -25 a - 43\bigr] \)
900.2-k2	\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 33 a - 98\) , \( 241 a - 664\bigr] \)