Properties

Base field 4.4.10512.1
Label 4.4.10512.1-4.1-a
Conductor 4.1
Rank not recorded

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Base field 4.4.10512.1

Generator \(a\), with minimal polynomial \( x^{4} - 7 x^{2} - 6 x + 1 \); class number \(1\).

Elliptic curves in class 4.1-a over 4.4.10512.1

Isogeny class 4.1-a contains 6 curves linked by isogenies of degrees dividing 45.

Curve label Weierstrass Coefficients
4.1-a1 \( \bigl[a^{2} - a - 4\) , \( a\) , \( a^{3} - 5 a - 5\) , \( 589 a^{3} + 152 a^{2} - 4327 a - 4831\) , \( 19288 a^{3} + 3575 a^{2} - 137422 a - 142859\bigr] \)
4.1-a2 \( \bigl[a^{2} - a - 4\) , \( a\) , \( a^{3} - 5 a - 5\) , \( -96 a^{3} + 122 a^{2} + 523 a - 91\) , \( -697 a^{3} + 877 a^{2} + 3789 a - 585\bigr] \)
4.1-a3 \( \bigl[a^{2} - a - 4\) , \( a\) , \( a^{3} - 5 a - 5\) , \( 29 a^{3} - 28 a^{2} - 147 a - 51\) , \( 12 a^{3} + 63 a^{2} - 206 a - 287\bigr] \)
4.1-a4 \( \bigl[a^{2} - a - 4\) , \( a\) , \( a^{3} - 5 a - 5\) , \( -a^{3} - 23 a^{2} - 42 a - 11\) , \( 31 a^{3} + 124 a^{2} + 104 a - 24\bigr] \)
4.1-a5 \( \bigl[a^{2} - a - 4\) , \( a\) , \( a^{3} - 5 a - 5\) , \( -a^{3} + 2 a^{2} + 3 a - 6\) , \( -2 a - 5\bigr] \)
4.1-a6 \( \bigl[a^{2} - a - 4\) , \( a\) , \( a^{3} - 5 a - 5\) , \( 689 a^{3} - 1428 a^{2} - 2067 a + 249\) , \( -23344 a^{3} + 45467 a^{2} + 77118 a - 12191\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 5 & 3 & 45 & 15 & 9 \\ 5 & 1 & 15 & 9 & 3 & 45 \\ 3 & 15 & 1 & 15 & 5 & 3 \\ 45 & 9 & 15 & 1 & 3 & 5 \\ 15 & 3 & 5 & 3 & 1 & 15 \\ 9 & 45 & 3 & 5 & 15 & 1 \end{array}\right)\)

Isogeny graph