Elliptic curve isogeny class 605.1-b over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-605.1-b
• Conductor: 605.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 605.1-b over \(\Q(\sqrt{5}) \)

Isogeny class 605.1-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
605.1-b1	\( \bigl[\phi\) , \( \phi - 1\) , \( 0\) , \( -3 \phi - 10\) , \( 1581 \phi - 2595\bigr] \)
605.1-b2	\( \bigl[\phi + 1\) , \( \phi\) , \( 0\) , \( 35 \phi - 34\) , \( -84 \phi + 119\bigr] \)
605.1-b3	\( \bigl[\phi + 1\) , \( \phi\) , \( 0\) , \( -4\) , \( -7 \phi - 2\bigr] \)
605.1-b4	\( \bigl[\phi + 1\) , \( \phi\) , \( 0\) , \( 1\) , \( 0\bigr] \)
605.1-b5	\( \bigl[\phi + 1\) , \( \phi\) , \( 0\) , \( -35 \phi - 54\) , \( -238 \phi - 211\bigr] \)
605.1-b6	\( \bigl[\phi + 1\) , \( \phi\) , \( 0\) , \( -585 \phi - 879\) , \( -12393 \phi - 12091\bigr] \)

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