Elliptic curve isogeny class 76.1-b over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-76.1-b
• Conductor: 76.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 76.1-b over \(\Q(\sqrt{5}) \)

Isogeny class 76.1-b contains 4 curves linked by isogenies of degrees dividing 27.

Curve label	Weierstrass Coefficients
76.1-b1	\( \bigl[\phi + 1\) , \( 0\) , \( 1\) , \( 3364 \phi - 15986\) , \( 229016 \phi - 793226\bigr] \)
76.1-b2	\( \bigl[\phi + 1\) , \( 0\) , \( 1\) , \( -\phi - 1\) , \( 0\bigr] \)
76.1-b3	\( \bigl[\phi + 1\) , \( 0\) , \( 1\) , \( 44 \phi - 196\) , \( 264 \phi - 1122\bigr] \)
76.1-b4	\( \bigl[\phi + 1\) , \( 0\) , \( 1\) , \( 4 \phi + 4\) , \( 8 \phi - 2\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 27 & 3 & 9 \\ 27 & 1 & 9 & 3 \\ 3 & 9 & 1 & 3 \\ 9 & 3 & 3 & 1 \end{array}\right)\)

Isogeny graph