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

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-900.2-v
• Conductor: 900.2
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

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

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

Curve label	Weierstrass Coefficients
900.2-v1	\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 4 a + 10\) , \( 39 a + 120\bigr] \)
900.2-v2	\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -56 a - 290\) , \( 339 a + 1620\bigr] \)