Elliptic curve isogeny class 9.1-b over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-9.1-b
• Conductor: 9.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{17}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 4 \); class number \(1\).

Elliptic curves in class 9.1-b over \(\Q(\sqrt{17}) \)

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

Curve label	Weierstrass Coefficients
9.1-b1	\( \bigl[0\) , \( -a\) , \( 1\) , \( 795 a - 2035\) , \( 17928 a - 45924\bigr] \)
9.1-b2	\( \bigl[0\) , \( -a\) , \( 1\) , \( -5 a + 15\) , \( 2 a - 6\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph