Elliptic curve isogeny class 3969.1-d over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-3969.1-d
• Conductor: 3969.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 3969.1-d over \(\Q(\sqrt{5}) \)

Isogeny class 3969.1-d contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
3969.1-d1	\( \bigl[1\) , \( -1\) , \( 0\) , \( -306\) , \( 5859\bigr] \)
3969.1-d2	\( \bigl[1\) , \( -1\) , \( 0\) , \( 9\) , \( 0\bigr] \)
3969.1-d3	\( \bigl[1\) , \( -1\) , \( 0\) , \( -36\) , \( 27\bigr] \)
3969.1-d4	\( \bigl[1\) , \( -1\) , \( 0\) , \( -351\) , \( -2430\bigr] \)
3969.1-d5	\( \bigl[1\) , \( -1\) , \( 0\) , \( -441\) , \( 3672\bigr] \)
3969.1-d6	\( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph