Elliptic curve isogeny class 199.2-a over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-199.2-a
• Conductor: 199.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 199.2-a over \(\Q(\sqrt{5}) \)

Isogeny class 199.2-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
199.2-a1	\( \bigl[0\) , \( 0\) , \( 1\) , \( -4 \phi - 5\) , \( 6 \phi + 5\bigr] \)
199.2-a2	\( \bigl[0\) , \( 0\) , \( 1\) , \( 76 \phi - 55\) , \( 174 \phi - 289\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph