Elliptic curve isogeny class 3751.6-f over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-3751.6-f
• Conductor: 3751.6
• Rank: \( 1 \)

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

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

Elliptic curves in class 3751.6-f over \(\Q(\sqrt{5}) \)

Isogeny class 3751.6-f contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
3751.6-f1	\( \bigl[\phi\) , \( -\phi\) , \( \phi + 1\) , \( -3 \phi + 2\) , \( -3 \phi + 3\bigr] \)
3751.6-f2	\( \bigl[\phi + 1\) , \( \phi - 1\) , \( \phi\) , \( 21 \phi + 9\) , \( 19 \phi + 6\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph