Properties

Base field 4.4.9248.1
Label 4.4.9248.1-8.3-a
Conductor 8.3
Rank \( 0 \)

Related objects

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Base field 4.4.9248.1

Generator \(a\), with minimal polynomial \( x^{4} - 5 x^{2} + 2 \); class number \(1\).

Elliptic curves in class 8.3-a over 4.4.9248.1

Isogeny class 8.3-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
8.3-a1 \( \bigl[a^{2} - 2\) , \( -a^{2} + 3\) , \( a^{2} - 2\) , \( 3 a^{2} - 17\) , \( -3 a^{2} + 12\bigr] \)
8.3-a2 \( \bigl[a\) , \( a^{2} - 4\) , \( 0\) , \( 4\) , \( a^{2} - 2\bigr] \)
8.3-a3 \( \bigl[a\) , \( a^{2} - 3\) , \( a\) , \( -a^{2} + 2\) , \( -a^{2}\bigr] \)
8.3-a4 \( \bigl[a\) , \( a^{2} - 3\) , \( a\) , \( -11 a^{2} + 7\) , \( -36 a^{2} + 15\bigr] \)
8.3-a5 \( \bigl[a\) , \( 0\) , \( a^{3} - 4 a\) , \( 425 a^{3} + 317 a^{2} - 1940 a - 1450\) , \( 8542 a^{3} + 5847 a^{2} - 38964 a - 26670\bigr] \)
8.3-a6 \( \bigl[a\) , \( 0\) , \( a^{3} - 4 a\) , \( -425 a^{3} + 317 a^{2} + 1940 a - 1450\) , \( -8542 a^{3} + 5847 a^{2} + 38964 a - 26670\bigr] \)
8.3-a7 \( \bigl[a\) , \( 0\) , \( a^{3} - 4 a\) , \( 37 a^{2} - 170\) , \( 181 a^{2} - 826\bigr] \)
8.3-a8 \( \bigl[a\) , \( 0\) , \( a^{3} - 4 a\) , \( 2 a^{2} - 10\) , \( 3 a^{2} - 14\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 8 & 2 & 4 & 16 & 16 & 8 & 4 \\ 8 & 1 & 4 & 8 & 8 & 8 & 4 & 2 \\ 2 & 4 & 1 & 2 & 8 & 8 & 4 & 2 \\ 4 & 8 & 2 & 1 & 16 & 16 & 8 & 4 \\ 16 & 8 & 8 & 16 & 1 & 4 & 2 & 4 \\ 16 & 8 & 8 & 16 & 4 & 1 & 2 & 4 \\ 8 & 4 & 4 & 8 & 2 & 2 & 1 & 2 \\ 4 & 2 & 2 & 4 & 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph