Elliptic curve isogeny class 169.2-b over number field \(\Q(\sqrt{-17}) \)

• Base field: \(\Q(\sqrt{-17}) \)
• Label: 2.0.68.1-169.2-b
• Conductor: 169.2
• Rank: \( 1 \)

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

Generator \(a\), with minimal polynomial \( x^{2} + 17 \); class number \(4\).

Elliptic curves in class 169.2-b over \(\Q(\sqrt{-17}) \)

Isogeny class 169.2-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
169.2-b1	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( a + 19\) , \( -10 a - 17\bigr] \)
169.2-b2	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( a + 279\) , \( -478 a - 277\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph