Elliptic curve isogeny class 605.3-c over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-605.3-c
• Conductor: 605.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 605.3-c over \(\Q(\sqrt{5}) \)

Isogeny class 605.3-c contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
605.3-c1	\( \bigl[\phi\) , \( -1\) , \( \phi\) , \( -\phi - 1\) , \( -\phi + 1\bigr] \)
605.3-c2	\( \bigl[\phi\) , \( -1\) , \( \phi\) , \( 4 \phi - 21\) , \( -14 \phi + 42\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph