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

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-199.2-c
• Conductor: 199.2
• Rank: \( 1 \)

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

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

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

Isogeny class 199.2-c contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
199.2-c1	\( \bigl[0\) , \( 1\) , \( 1\) , \( -392 \phi - 441\) , \( -5756 \phi - 4705\bigr] \)
199.2-c2	\( \bigl[0\) , \( -\phi - 1\) , \( 1\) , \( \phi\) , \( 0\bigr] \)
199.2-c3	\( \bigl[0\) , \( -\phi - 1\) , \( 1\) , \( 11 \phi - 10\) , \( 6 \phi - 21\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph