Elliptic curve isogeny class 3025.1-a over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-3025.1-a
• Conductor: 3025.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 3025.1-a over \(\Q(\sqrt{5}) \)

Isogeny class 3025.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
3025.1-a1	\( \bigl[1\) , \( 0\) , \( \phi + 1\) , \( 82 \phi - 151\) , \( 3583 \phi + 3639\bigr] \)
3025.1-a2	\( \bigl[1\) , \( 0\) , \( \phi + 1\) , \( 7 \phi - 1\) , \( -2 \phi - 6\bigr] \)
3025.1-a3	\( \bigl[1\) , \( 0\) , \( \phi + 1\) , \( -18 \phi - 26\) , \( -42 \phi - 11\bigr] \)
3025.1-a4	\( \bigl[1\) , \( 0\) , \( \phi + 1\) , \( -93 \phi - 276\) , \( 923 \phi + 1794\bigr] \)
3025.1-a5	\( \bigl[\phi + 1\) , \( -\phi\) , \( \phi + 1\) , \( -160 \phi + 149\) , \( -1048 \phi + 1268\bigr] \)
3025.1-a6	\( \bigl[1\) , \( 0\) , \( \phi + 1\) , \( -1468 \phi - 4401\) , \( 60323 \phi + 116469\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph