Properties

Base field \(\Q(\sqrt{2}, \sqrt{3})\)
Label 4.4.2304.1-47.1-b
Conductor 47.1
Rank not recorded

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Base field \(\Q(\sqrt{2}, \sqrt{3})\)

Generator \(a\), with minimal polynomial \( x^{4} - 4 x^{2} + 1 \); class number \(1\).

Elliptic curves in class 47.1-b over \(\Q(\sqrt{2}, \sqrt{3})\)

Isogeny class 47.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
47.1-b1 \( \bigl[a^{2} - 1\) , \( a^{3} + a^{2} - 5 a - 1\) , \( a^{2} + a - 1\) , \( -3 a^{3} + a^{2} + 8 a - 1\) , \( -2 a\bigr] \)
47.1-b2 \( \bigl[a^{3} - 4 a + 1\) , \( a^{2} - 2\) , \( a^{3} - 4 a\) , \( -2 a^{3} - 3 a^{2} + a\) , \( 2 a^{3} + 5 a^{2} + a - 2\bigr] \)
47.1-b3 \( \bigl[a^{2} - 1\) , \( -a^{3} + a^{2} + 5 a - 2\) , \( a^{2} + a - 1\) , \( a^{3} - 2 a + 1\) , \( 0\bigr] \)
47.1-b4 \( \bigl[a^{2} + a - 2\) , \( -a^{2} - a + 3\) , \( a^{3} - 3 a + 1\) , \( 3 a^{3} - a^{2} - 17 a - 7\) , \( -12 a^{3} - 4 a^{2} + 36 a - 2\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph