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

• Base field: \(\Q(\sqrt{105}) \)
• Label: 2.2.105.1-9.1-a
• 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-a over \(\Q(\sqrt{105}) \)

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

Curve label	Weierstrass Coefficients
9.1-a1	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 50422 a - 283550\) , \( 17141097 a - 96392548\bigr] \)
9.1-a2	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 5690590 a - 32000905\) , \( -20545570618 a + 115537510593\bigr] \)
9.1-a3	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 857182 a - 4820345\) , \( 977546796 a - 5497210354\bigr] \)
9.1-a4	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 96740095 a - 544015555\) , \( -1171929687574 a + 6590317748649\bigr] \)

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