Elliptic curve isogeny class 1089.1-b over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-1089.1-b
• Conductor: 1089.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{5}) \)

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

Elliptic curves in class 1089.1-b over \(\Q(\sqrt{5}) \)

Isogeny class 1089.1-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
1089.1-b1	\( \bigl[\phi + 1\) , \( \phi + 1\) , \( 0\) , \( 4 \phi\) , \( \phi + 2\bigr] \)
1089.1-b2	\( \bigl[1\) , \( -\phi\) , \( 1\) , \( -14 \phi - 15\) , \( 44 \phi + 31\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph