Elliptic curve isogeny class 3025.3-b over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-3025.3-b
• Conductor: 3025.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 3025.3-b over \(\Q(\sqrt{5}) \)

Isogeny class 3025.3-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
3025.3-b1	\( \bigl[1\) , \( 1\) , \( \phi\) , \( -8 \phi - 5\) , \( \phi - 4\bigr] \)
3025.3-b2	\( \bigl[1\) , \( 1\) , \( \phi\) , \( -58 \phi - 80\) , \( -364 \phi - 359\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph