Elliptic curve isogeny class 961.3-c over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-961.3-c
• Conductor: 961.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 961.3-c over \(\Q(\sqrt{5}) \)

Isogeny class 961.3-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
961.3-c1	\( \bigl[\phi\) , \( 0\) , \( 0\) , \( -652 \phi - 1396\) , \( -27054 \phi - 5575\bigr] \)
961.3-c2	\( \bigl[\phi + 1\) , \( 0\) , \( 0\) , \( 497 \phi - 153\) , \( -20816 \phi - 16670\bigr] \)
961.3-c3	\( \bigl[\phi\) , \( 0\) , \( 0\) , \( -7 \phi - 16\) , \( 24 \phi - 4\bigr] \)
961.3-c4	\( \bigl[\phi\) , \( 0\) , \( 0\) , \( 18 \phi - 186\) , \( 140 \phi - 985\bigr] \)
961.3-c5	\( \bigl[1\) , \( 0\) , \( 0\) , \( 474 \phi - 1129\) , \( 6456 \phi - 13128\bigr] \)
961.3-c6	\( \bigl[1\) , \( 0\) , \( 0\) , \( -3856 \phi + 446\) , \( -31874 \phi - 118625\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 8 & 4 & 2 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 8 & 4 & 1 & 2 & 4 & 8 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 2 & 4 & 4 & 2 & 1 & 2 \\ 4 & 8 & 8 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph