Elliptic curve isogeny class 441.1-a over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-441.1-a
• Conductor: 441.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 441.1-a over \(\Q(\sqrt{21}) \)

Isogeny class 441.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
441.1-a1	\( \bigl[1\) , \( a\) , \( 1\) , \( 151 a - 421\) , \( 5254 a - 14668\bigr] \)
441.1-a2	\( \bigl[1\) , \( a\) , \( 1\) , \( 3826 a - 10711\) , \( 193120 a - 539164\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph