Properties

Base field 4.4.2777.1
Label 4.4.2777.1-22.1-c
Conductor 22.1
Rank not recorded

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Base field 4.4.2777.1

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

Elliptic curves in class 22.1-c over 4.4.2777.1

Isogeny class 22.1-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
22.1-c1 \( \bigl[a^{3} - 4 a - 1\) , \( -a^{2} + 2 a + 2\) , \( a^{3} - a^{2} - 3 a + 1\) , \( -5 a^{3} + 4 a^{2} + 18 a - 5\) , \( -4 a + 10\bigr] \)
22.1-c2 \( \bigl[a^{3} - 4 a - 1\) , \( -a^{2} + 2 a + 2\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 5 a^{3} - 46 a^{2} + 23 a + 25\) , \( -76 a^{3} + 260 a^{2} + 9 a - 124\bigr] \)
22.1-c3 \( \bigl[a^{3} - 3 a - 1\) , \( a^{2} - a - 3\) , \( a^{2} - a - 2\) , \( 63 a^{3} - 9 a^{2} - 267 a - 166\) , \( 458 a^{3} - 86 a^{2} - 1890 a - 1084\bigr] \)
22.1-c4 \( \bigl[a^{2} - 1\) , \( a^{2} - 2 a - 1\) , \( 0\) , \( 4 a^{3} - 4 a^{2} - 4 a\) , \( 15 a^{3} - 18 a^{2} - a + 12\bigr] \)
22.1-c5 \( \bigl[a^{2} - 1\) , \( a^{2} - 2 a - 1\) , \( 0\) , \( -a^{3} + a^{2} + a\) , \( 0\bigr] \)
22.1-c6 \( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( a^{3} - 2 a^{2} - 3 a + 4\) , \( a^{3} - 3 a - 1\) , \( 3 a^{3} - 5 a^{2} - 10 a + 8\) , \( 2 a^{3} - 4 a^{2} - 7 a + 6\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph