Properties

Base field 4.4.11324.1
Label 4.4.11324.1-8.1-d
Conductor 8.1
Rank \( 0 \)

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Base field 4.4.11324.1

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

Elliptic curves in class 8.1-d over 4.4.11324.1

Isogeny class 8.1-d contains 3 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
8.1-d1 \( \bigl[1\) , \( a^{2} + a - 3\) , \( a^{3} - 4 a + 1\) , \( a^{3} + 3 a^{2} - 4 a\) , \( 2 a^{2} - a - 3\bigr] \)
8.1-d2 \( \bigl[1\) , \( a^{2} + a - 3\) , \( a^{3} - 4 a + 1\) , \( -14 a^{3} - 47 a^{2} + 36 a + 20\) , \( -169 a^{3} - 350 a^{2} + 445 a + 193\bigr] \)
8.1-d3 \( \bigl[1\) , \( a^{2} + a - 3\) , \( a^{3} - 4 a + 1\) , \( -1149 a^{3} - 3922 a^{2} + 3071 a + 1540\) , \( -99521 a^{3} - 216742 a^{2} + 264677 a + 117393\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph