Properties

Base field 4.4.8112.1
Label 4.4.8112.1-9.1-b
Conductor 9.1
Rank \( 0 \)

Related objects

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Base field 4.4.8112.1

Generator \(a\), with minimal polynomial \( x^{4} - 5 x^{2} + 3 \); class number \(1\).

Elliptic curves in class 9.1-b over 4.4.8112.1

Isogeny class 9.1-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
9.1-b1 \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{3} + a^{2} - 3 a - 4\) , \( a^{3} - 4 a\) , \( 2 a^{3} + 4 a^{2} - 4 a - 6\) , \( -a^{3} + 6 a + 3\bigr] \)
9.1-b2 \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{3} + a^{2} + 3 a - 4\) , \( 1\) , \( a^{3} - a^{2} - 3 a + 4\) , \( 2 a^{3} - 2 a^{2} - 6 a + 5\bigr] \)
9.1-b3 \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -1\) , \( a^{3} + a^{2} - 3 a - 3\) , \( 27 a^{3} + 22 a^{2} - 116 a - 96\) , \( 127 a^{3} + 106 a^{2} - 546 a - 456\bigr] \)
9.1-b4 \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -1\) , \( a^{2} + a - 2\) , \( -26 a^{3} + 21 a^{2} + 111 a - 92\) , \( -105 a^{3} + 87 a^{2} + 451 a - 376\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 6 & 3 \\ 2 & 1 & 3 & 6 \\ 6 & 3 & 1 & 2 \\ 3 & 6 & 2 & 1 \end{array}\right)\)

Isogeny graph