Elliptic curve isogeny class 1089.3-b over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-1089.3-b
• Conductor: 1089.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 1089.3-b over \(\Q(\sqrt{5}) \)

Isogeny class 1089.3-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
1089.3-b1	\( \bigl[1\) , \( 1\) , \( \phi + 1\) , \( 2081 \phi - 4539\) , \( 84429 \phi - 121384\bigr] \)
1089.3-b2	\( \bigl[1\) , \( 1\) , \( \phi + 1\) , \( -4 \phi + 6\) , \( 3 \phi + 5\bigr] \)
1089.3-b3	\( \bigl[1\) , \( 1\) , \( \phi + 1\) , \( 86 \phi - 299\) , \( -1286 \phi + 1597\bigr] \)
1089.3-b4	\( \bigl[1\) , \( 1\) , \( \phi + 1\) , \( -19 \phi - 44\) , \( 100 \phi + 46\bigr] \)
1089.3-b5	\( \bigl[1\) , \( 1\) , \( \phi + 1\) , \( -364 \phi - 589\) , \( 7994 \phi + 2119\bigr] \)
1089.3-b6	\( \bigl[\phi + 1\) , \( \phi - 1\) , \( 1\) , \( -580 \phi - 1809\) , \( 63014 \phi - 48649\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 8 & 4 & 2 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 8 & 4 & 1 & 2 & 4 & 8 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 2 & 4 & 4 & 2 & 1 & 2 \\ 4 & 8 & 8 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph