Elliptic curve isogeny class 3600.1-d over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-3600.1-d
• Conductor: 3600.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 3600.1-d over \(\Q(\sqrt{5}) \)

Isogeny class 3600.1-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
3600.1-d1	\( \bigl[0\) , \( -1\) , \( 0\) , \( 12\) , \( 72\bigr] \)
3600.1-d2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 75 \phi - 163\) , \( -585 \phi + 877\bigr] \)
3600.1-d3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -13\) , \( 22\bigr] \)
3600.1-d4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -75 \phi - 88\) , \( 585 \phi + 292\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph