Elliptic curve isogeny class 171.2-a over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-171.2-a
• Conductor: 171.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 171.2-a over \(\Q(\sqrt{5}) \)

Isogeny class 171.2-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
171.2-a1	\( \bigl[\phi\) , \( \phi + 1\) , \( \phi + 1\) , \( -28 \phi + 13\) , \( 15 \phi - 137\bigr] \)
171.2-a2	\( \bigl[\phi + 1\) , \( -1\) , \( 1\) , \( -\phi - 1\) , \( -2 \phi - 1\bigr] \)
171.2-a3	\( \bigl[\phi + 1\) , \( -1\) , \( 1\) , \( -16 \phi - 21\) , \( -66 \phi - 23\bigr] \)
171.2-a4	\( \bigl[\phi\) , \( \phi + 1\) , \( \phi + 1\) , \( -103 \phi - 372\) , \( -1584 \phi - 2858\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph