Elliptic curve isogeny class 4225.1-b over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-4225.1-b
• Conductor: 4225.1
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 4225.1-b over \(\Q(\sqrt{5}) \)

Isogeny class 4225.1-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
4225.1-b1	\( \bigl[0\) , \( -\phi\) , \( 1\) , \( 17 \phi - 33\) , \( 49 \phi - 82\bigr] \)
4225.1-b2	\( \bigl[0\) , \( -\phi\) , \( 1\) , \( 267 \phi - 533\) , \( -2901 \phi + 5143\bigr] \)