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

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

Isogeny class 9.1-f contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
9.1-f1	\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( -198 a - 1230\) , \( 4334 a + 25428\bigr] \)
9.1-f2	\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( 2 a + 20\) , \( -4 a - 24\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph