Elliptic curve isogeny class 205.2-c over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-205.2-c
• Conductor: 205.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 205.2-c over \(\Q(\sqrt{5}) \)

Isogeny class 205.2-c contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
205.2-c1	\( \bigl[\phi\) , \( -\phi + 1\) , \( \phi + 1\) , \( -10 \phi + 13\) , \( -7 \phi + 7\bigr] \)
205.2-c2	\( \bigl[\phi + 1\) , \( -\phi\) , \( \phi + 1\) , \( -\phi - 1\) , \( 0\bigr] \)
205.2-c3	\( \bigl[\phi + 1\) , \( -\phi\) , \( \phi + 1\) , \( -6 \phi - 11\) , \( 8 \phi + 11\bigr] \)
205.2-c4	\( \bigl[\phi\) , \( -\phi + 1\) , \( \phi + 1\) , \( 15 \phi - 62\) , \( -22 \phi - 48\bigr] \)

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