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

• Base field: \(\Q(\sqrt{34}) \)
• Label: 2.2.136.1-9.1-b
• 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-b over \(\Q(\sqrt{34}) \)

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

Curve label	Weierstrass Coefficients
9.1-b1	\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 114 a - 684\) , \( -1292 a + 7522\bigr] \)
9.1-b2	\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -6 a + 16\) , \( -3 a + 6\bigr] \)
9.1-b3	\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 26939 a - 157082\) , \( 5753558 a - 33548720\bigr] \)
9.1-b4	\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 2378459 a - 13868682\) , \( -4810865707 a + 28051926510\bigr] \)

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