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

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-3751.6-d
• Conductor: 3751.6
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
3751.6-d1	\( \bigl[1\) , \( -\phi\) , \( \phi\) , \( 11 \phi + 2\) , \( -14 \phi - 12\bigr] \)
3751.6-d2	\( \bigl[1\) , \( -\phi\) , \( \phi\) , \( -54 \phi - 13\) , \( -75 \phi - 54\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph