Elliptic curve isogeny class 1600.1-l over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-1600.1-l
• Conductor: 1600.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 1600.1-l over \(\Q(\sqrt{5}) \)

Isogeny class 1600.1-l contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
1600.1-l1	\( \bigl[0\) , \( \phi + 1\) , \( 0\) , \( -119 \phi - 421\) , \( 3319 \phi + 4500\bigr] \)
1600.1-l2	\( \bigl[0\) , \( 1\) , \( 0\) , \( 2\) , \( 5 \phi - 7\bigr] \)
1600.1-l3	\( \bigl[0\) , \( \phi + 1\) , \( 0\) , \( -19 \phi - 21\) , \( 19 \phi\bigr] \)
1600.1-l4	\( \bigl[0\) , \( \phi + 1\) , \( 0\) , \( -119 \phi - 221\) , \( -1281 \phi - 1500\bigr] \)
1600.1-l5	\( \bigl[0\) , \( 1\) , \( 0\) , \( 25 \phi - 148\) , \( -45 \phi + 468\bigr] \)
1600.1-l6	\( \bigl[0\) , \( 1\) , \( 0\) , \( -975 \phi - 148\) , \( 10355 \phi + 10268\bigr] \)

Rank

Rank: \( 0 \)

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