Elliptic curve isogeny class 1025.2-a over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-1025.2-a
• Conductor: 1025.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 1025.2-a over \(\Q(\sqrt{5}) \)

Isogeny class 1025.2-a contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
1025.2-a1	\( \bigl[0\) , \( 1\) , \( \phi + 1\) , \( 105 \phi - 258\) , \( -1417 \phi + 2585\bigr] \)
1025.2-a2	\( \bigl[0\) , \( \phi + 1\) , \( \phi + 1\) , \( \phi - 1\) , \( -3 \phi - 3\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph