Elliptic curve isogeny class 9.1-b over number field \(\Q(\sqrt{105}) \)

• Base field: \(\Q(\sqrt{105}) \)
• Label: 2.2.105.1-9.1-b
• Conductor: 9.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{105}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 26 \); class number \(2\).

Elliptic curves in class 9.1-b over \(\Q(\sqrt{105}) \)

Isogeny class 9.1-b contains 4 curves linked by isogenies of degrees dividing 14.

Curve label	Weierstrass Coefficients
9.1-b1	\( \bigl[1\) , \( -1\) , \( a\) , \( 7 a - 42\) , \( 29 a - 171\bigr] \)
9.1-b2	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 843 a - 4737\) , \( -34227 a + 192476\bigr] \)
9.1-b3	\( \bigl[1\) , \( -1\) , \( a\) , \( 127 a - 717\) , \( 1742 a - 9804\bigr] \)
9.1-b4	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 14388 a - 80907\) , \( -2074476 a + 11665766\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 7 & 2 & 14 \\ 7 & 1 & 14 & 2 \\ 2 & 14 & 1 & 7 \\ 14 & 2 & 7 & 1 \end{array}\right)\)

Isogeny graph