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

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-605.1-a
• 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-a over \(\Q(\sqrt{5}) \)

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

Curve label	Weierstrass Coefficients
605.1-a1	\( \bigl[\phi + 1\) , \( \phi\) , \( 1\) , \( 4 \phi - 13\) , \( -1591 \phi - 1011\bigr] \)
605.1-a2	\( \bigl[\phi\) , \( \phi - 1\) , \( 1\) , \( \phi - 1\) , \( -\phi + 2\bigr] \)
605.1-a3	\( \bigl[\phi\) , \( \phi - 1\) , \( 1\) , \( \phi - 6\) , \( \phi - 2\bigr] \)
605.1-a4	\( \bigl[\phi\) , \( \phi - 1\) , \( 1\) , \( 36 \phi - 91\) , \( 147 \phi - 322\bigr] \)
605.1-a5	\( \bigl[\phi\) , \( \phi - 1\) , \( 1\) , \( -34 \phi - 1\) , \( 83 \phi + 2\bigr] \)
605.1-a6	\( \bigl[\phi\) , \( \phi - 1\) , \( 1\) , \( 586 \phi - 1466\) , \( 10927 \phi - 22432\bigr] \)

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