Elliptic curve isogeny class 900.3-r over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-900.3-r
• Conductor: 900.3
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 900.3-r over \(\Q(\sqrt{21}) \)

Isogeny class 900.3-r contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
900.3-r1	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -2 a - 92\) , \( 6 a + 328\bigr] \)
900.3-r2	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 3 a + 3\) , \( 2 a + 2\bigr] \)