Elliptic curve isogeny class 2511.2-f over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-2511.2-f
• Conductor: 2511.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 2511.2-f over \(\Q(\sqrt{5}) \)

Isogeny class 2511.2-f contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
2511.2-f1	\( \bigl[1\) , \( -1\) , \( 1\) , \( -273 \phi - 410\) , \( 3940 \phi + 3831\bigr] \)
2511.2-f2	\( \bigl[\phi\) , \( -\phi - 1\) , \( 1\) , \( 151 \phi - 18\) , \( 4776 \phi + 2508\bigr] \)
2511.2-f3	\( \bigl[1\) , \( -1\) , \( 1\) , \( -3 \phi - 5\) , \( -2 \phi - 3\bigr] \)
2511.2-f4	\( \bigl[1\) , \( -1\) , \( 1\) , \( -3 \phi - 50\) , \( 124 \phi - 39\bigr] \)
2511.2-f5	\( \bigl[\phi + 1\) , \( 1\) , \( \phi\) , \( 98 \phi - 284\) , \( 1154 \phi - 1438\bigr] \)
2511.2-f6	\( \bigl[\phi + 1\) , \( 1\) , \( \phi\) , \( -1207 \phi - 59\) , \( 19919 \phi + 695\bigr] \)

Rank

Rank: \( 0 \)

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