Elliptic curve isogeny class 8.1-b over number field \(\Q(\sqrt{34}) \)

• Base field: \(\Q(\sqrt{34}) \)
• Label: 2.2.136.1-8.1-b
• Conductor: 8.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 8.1-b over \(\Q(\sqrt{34}) \)

Isogeny class 8.1-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
8.1-b1	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -8 a + 31\) , \( -12 a + 60\bigr] \)
8.1-b2	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -28 a - 94\) , \( 104 a + 704\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph