Properties

Base field \(\Q(\sqrt{2}, \sqrt{5})\)
Label 4.4.1600.1-400.1-a
Conductor 400.1
Rank not recorded

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Base field \(\Q(\sqrt{2}, \sqrt{5})\)

Generator \(a\), with minimal polynomial \( x^{4} - 6 x^{2} + 4 \); class number \(1\).

Elliptic curves in class 400.1-a over \(\Q(\sqrt{2}, \sqrt{5})\)

Isogeny class 400.1-a contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
400.1-a1 \( \bigl[a\) , \( -\frac{1}{2} a^{2}\) , \( 0\) , \( \frac{25}{2} a^{2} - 89\) , \( 29 a^{2} - 187\bigr] \)
400.1-a2 \( \bigl[a\) , \( \frac{1}{2} a^{2} - 1\) , \( a\) , \( -\frac{1}{2} a^{2} - 2\) , \( -1\bigr] \)
400.1-a3 \( \bigl[\frac{1}{2} a^{3} - 2 a\) , \( 0\) , \( \frac{1}{2} a^{3} - 2 a\) , \( -10\) , \( -18\bigr] \)
400.1-a4 \( \bigl[\frac{1}{2} a^{3} - 2 a\) , \( 0\) , \( \frac{1}{2} a^{3} - 2 a\) , \( 0\) , \( 0\bigr] \)
400.1-a5 \( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 0\bigr] \)
400.1-a6 \( \bigl[0\) , \( 1\) , \( 0\) , \( -41\) , \( -116\bigr] \)
400.1-a7 \( \bigl[\frac{1}{2} a^{3} - a\) , \( 1\) , \( a\) , \( a^{2} - 5\) , \( -a^{2} + 3\bigr] \)
400.1-a8 \( \bigl[\frac{1}{2} a^{3} - a\) , \( -\frac{1}{2} a^{2} + 2\) , \( \frac{1}{2} a^{3} - a\) , \( -\frac{27}{2} a^{2} - 13\) , \( -42 a^{2} - 27\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph