Properties

Base field 4.4.4752.1
Label 4.4.4752.1-9.1-c
Conductor 9.1
Rank not recorded

Related objects

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Base field 4.4.4752.1

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

Elliptic curves in class 9.1-c over 4.4.4752.1

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

Curve label Weierstrass Coefficients
9.1-c1 \( \bigl[a^{3} - 4 a - 1\) , \( a^{3} - 5 a - 2\) , \( a^{3} - 3 a\) , \( 3 a^{3} - 9 a^{2} + 4\) , \( 5 a^{3} - 20 a^{2} + 15 a + 2\bigr] \)
9.1-c2 \( \bigl[a^{3} - 4 a - 1\) , \( -a^{3} + 2 a^{2} + 2 a - 2\) , \( a^{2} - 1\) , \( 9 a^{3} - 8 a^{2} - 35 a - 6\) , \( -20 a^{3} + 14 a^{2} + 82 a + 17\bigr] \)
9.1-c3 \( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a^{3} - a^{2} - 2 a\) , \( a + 1\) , \( -11 a^{3} + 26 a^{2} + 28 a - 51\) , \( 33 a^{3} - 73 a^{2} - 83 a + 149\bigr] \)
9.1-c4 \( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a^{3} + 3 a + 2\) , \( a\) , \( -4 a^{3} + 11 a + 4\) , \( -4 a^{3} + 10 a + 1\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph