Elliptic curve isogeny class 9.1-e over number field \(\Q(\sqrt{34}) \)

• Base field: \(\Q(\sqrt{34}) \)
• Label: 2.2.136.1-9.1-e
• Conductor: 9.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{34}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 34 \); class number \(2\).

Elliptic curves in class 9.1-e over \(\Q(\sqrt{34}) \)

Isogeny class 9.1-e contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
9.1-e1	\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( 585435 a - 3413604\) , \( -621874868 a + 3626122516\bigr] \)
9.1-e2	\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( -2445 a + 14296\) , \( 2477531 a - 14446288\bigr] \)
9.1-e3	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 131974160 a - 769534922\) , \( 1931295231412 a - 11261289589020\bigr] \)
9.1-e4	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 11649718640 a - 67928948922\) , \( -1652733141687323 a + 9637007444195410\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph