Properties

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

Related objects

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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