Properties

Base field 4.4.13068.1
Label 4.4.13068.1-1.1-a
Conductor 1.1
Rank \( 0 \)

Related objects

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Base field 4.4.13068.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 6 x^{2} - x + 1 \); class number \(1\).

Elliptic curves in class 1.1-a over 4.4.13068.1

Isogeny class 1.1-a contains 6 curves linked by isogenies of degrees dividing 99.

Curve label Weierstrass Coefficients
1.1-a1 \( \bigl[0\) , \( -a^{3} + 2 a^{2} + 4 a - 1\) , \( 1\) , \( -714 a^{3} + 2020 a^{2} + 596 a - 394\) , \( -11736 a^{3} + 33145 a^{2} + 9957 a - 6439\bigr] \)
1.1-a2 \( \bigl[0\) , \( a^{3} - a^{2} - 6 a - 2\) , \( 1\) , \( -13 a^{3} + 64 a^{2} + 149 a - 20\) , \( -23 a^{3} + 212 a^{2} + 374 a - 163\bigr] \)
1.1-a3 \( \bigl[0\) , \( a^{3} - a^{2} - 7 a - 1\) , \( 1\) , \( -25 a^{3} + 25 a^{2} + 175 a + 85\) , \( 72 a^{3} - 72 a^{2} - 504 a - 243\bigr] \)
1.1-a4 \( \bigl[0\) , \( a^{3} - a^{2} - 6 a - 2\) , \( 1\) , \( -3 a^{3} - 6 a^{2} - a\) , \( 13 a^{3} + 34 a^{2} + 20 a + 2\bigr] \)
1.1-a5 \( \bigl[0\) , \( -a^{3} + 2 a^{2} + 4 a - 1\) , \( 1\) , \( 156 a^{3} - 440 a^{2} - 134 a + 86\) , \( -2586 a^{3} + 7303 a^{2} + 2195 a - 1418\bigr] \)
1.1-a6 \( \bigl[0\) , \( -a^{3} + a^{2} + 7 a\) , \( 1\) , \( 25 a^{3} - 25 a^{2} - 175 a + 60\) , \( -72 a^{3} + 72 a^{2} + 504 a - 171\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 11 & 9 & 33 & 3 & 99 \\ 11 & 1 & 99 & 3 & 33 & 9 \\ 9 & 99 & 1 & 33 & 3 & 11 \\ 33 & 3 & 33 & 1 & 11 & 3 \\ 3 & 33 & 3 & 11 & 1 & 33 \\ 99 & 9 & 11 & 3 & 33 & 1 \end{array}\right)\)

Isogeny graph