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

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-1600.1-i
• 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-i over \(\Q(\sqrt{5}) \)

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

Curve label	Weierstrass Coefficients
1600.1-i1	\( \bigl[0\) , \( 1\) , \( 0\) , \( 2\) , \( -5 \phi - 2\bigr] \)
1600.1-i2	\( \bigl[0\) , \( 1\) , \( 0\) , \( 975 \phi - 1123\) , \( -10355 \phi + 20623\bigr] \)
1600.1-i3	\( \bigl[0\) , \( 1\) , \( 0\) , \( -25 \phi - 123\) , \( 45 \phi + 423\bigr] \)
1600.1-i4	\( \bigl[0\) , \( -\phi - 1\) , \( 0\) , \( 21 \phi - 41\) , \( -39 \phi + 60\bigr] \)
1600.1-i5	\( \bigl[0\) , \( -\phi - 1\) , \( 0\) , \( 121 \phi - 541\) , \( -3439 \phi + 8360\bigr] \)
1600.1-i6	\( \bigl[0\) , \( -\phi - 1\) , \( 0\) , \( 121 \phi - 341\) , \( 1161 \phi - 2440\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph