Properties

Base field \(\Q(\sqrt{5}) \)
Label 2.2.5.1-900.1-b
Conductor 900.1
Rank \( 0 \)

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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 900.1-b over \(\Q(\sqrt{5}) \)

Isogeny class 900.1-b contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
900.1-b1 \( \bigl[\phi\) , \( -1\) , \( 1\) , \( 67 \phi - 135\) , \( -1275 \phi + 2231\bigr] \)
900.1-b2 \( \bigl[\phi\) , \( -1\) , \( 1\) , \( -8 \phi + 15\) , \( 45 \phi - 79\bigr] \)
900.1-b3 \( \bigl[\phi\) , \( -1\) , \( 1\) , \( 2267 \phi - 4535\) , \( -10875 \phi + 19031\bigr] \)
900.1-b4 \( \bigl[\phi + 1\) , \( -\phi - 1\) , \( 1\) , \( -343 \phi - 343\) , \( 3875 \phi + 2906\bigr] \)
900.1-b5 \( \bigl[\phi + 1\) , \( -\phi - 1\) , \( 1\) , \( -93 \phi - 93\) , \( -525 \phi - 394\bigr] \)
900.1-b6 \( \bigl[\phi + 1\) , \( -\phi - 1\) , \( 1\) , \( -1668 \phi - 1668\) , \( 47355 \phi + 35516\bigr] \)
900.1-b7 \( \bigl[\phi + 1\) , \( -\phi - 1\) , \( 1\) , \( -1443 \phi - 1443\) , \( -37245 \phi - 27934\bigr] \)
900.1-b8 \( \bigl[\phi + 1\) , \( -\phi - 1\) , \( 1\) , \( -26668 \phi - 26668\) , \( 3007355 \phi + 2255516\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 4 & 12 & 6 & 2 & 12 & 4 \\ 3 & 1 & 12 & 4 & 2 & 6 & 4 & 12 \\ 4 & 12 & 1 & 12 & 6 & 2 & 3 & 4 \\ 12 & 4 & 12 & 1 & 2 & 6 & 4 & 3 \\ 6 & 2 & 6 & 2 & 1 & 3 & 2 & 6 \\ 2 & 6 & 2 & 6 & 3 & 1 & 6 & 2 \\ 12 & 4 & 3 & 4 & 2 & 6 & 1 & 12 \\ 4 & 12 & 4 & 3 & 6 & 2 & 12 & 1 \end{array}\right)\)

Isogeny graph