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

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-441.1-b
• Conductor: 441.1
• Rank: \( 1 \)

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

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

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

Isogeny class 441.1-b contains 2 curves linked by isogenies of degree 13.

Curve label	Weierstrass Coefficients
441.1-b1	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -2736 a - 5472\) , \( 131031 a + 229304\bigr] \)
441.1-b2	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -6 a - 12\) , \( -9 a - 16\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)

Isogeny graph