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

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-3751.6-c
• 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-c over \(\Q(\sqrt{5}) \)

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

Curve label	Weierstrass Coefficients
3751.6-c1	\( \bigl[\phi + 1\) , \( -1\) , \( 0\) , \( -20 \phi + 17\) , \( -28 \phi + 67\bigr] \)
3751.6-c2	\( \bigl[1\) , \( \phi\) , \( 0\) , \( 306 \phi + 149\) , \( 177 \phi - 74\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph