Elliptic curve isogeny class 605.2-c over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-605.2-c
• Conductor: 605.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 605.2-c over \(\Q(\sqrt{5}) \)

Isogeny class 605.2-c contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
605.2-c1	\( \bigl[\phi + 1\) , \( -\phi - 1\) , \( \phi + 1\) , \( -\phi - 2\) , \( 0\bigr] \)
605.2-c2	\( \bigl[\phi + 1\) , \( -\phi - 1\) , \( \phi + 1\) , \( -6 \phi - 17\) , \( 13 \phi + 28\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph