Elliptic curve isogeny class 121.1-d over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-121.1-d
• Conductor: 121.1
• 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 121.1-d over \(\Q(\sqrt{21}) \)

Isogeny class 121.1-d contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
121.1-d1	\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 4 a + 5\) , \( 3 a + 6\bigr] \)
121.1-d2	\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 9 a - 10\) , \( 13 a - 24\bigr] \)