Properties

Base field \(\Q(\sqrt{2}, \sqrt{3})\)
Label 4.4.2304.1-46.3-a
Conductor 46.3
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 46.3-a over \(\Q(\sqrt{2}, \sqrt{3})\)

Isogeny class 46.3-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
46.3-a1 \( \bigl[a^{2} + a - 1\) , \( -a^{2} + a + 1\) , \( a^{3} - 3 a\) , \( 14 a^{3} + 28 a^{2} - 103 a - 60\) , \( -146 a^{3} + 37 a^{2} + 419 a + 187\bigr] \)
46.3-a2 \( \bigl[a\) , \( -a + 1\) , \( a^{2} + a - 1\) , \( -a^{3} + a\) , \( 9 a^{3} + 18 a^{2} - 2 a - 5\bigr] \)
46.3-a3 \( \bigl[1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( 11 a^{3} + 6 a^{2} - 40 a - 23\) , \( 32 a^{3} - a^{2} - 138 a - 33\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph