Properties

Base field 4.4.11324.1
Label 4.4.11324.1-8.1-c
Conductor 8.1
Rank \( 1 \)

Related objects

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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-c over 4.4.11324.1

Isogeny class 8.1-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
8.1-c1 \( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( -a^{3} - a^{2} + 3 a + 3\) , \( a\) , \( -7 a^{3} + 32 a + 4\) , \( -5 a^{3} - 2 a^{2} + 24 a + 12\bigr] \)
8.1-c2 \( \bigl[a^{3} + a^{2} - 3 a - 3\) , \( a^{2} + a - 3\) , \( a^{3} - 4 a\) , \( 242 a^{3} - 718 a^{2} + 323 a + 220\) , \( 6877 a^{3} - 21198 a^{2} + 9972 a + 6560\bigr] \)
8.1-c3 \( \bigl[a^{3} - 3 a + 1\) , \( -a^{3} + a^{2} + 3 a - 2\) , \( a^{3} - 4 a + 1\) , \( -a^{3} + a^{2} - 1\) , \( -3 a^{3} - 2 a^{2} + 5 a\bigr] \)
8.1-c4 \( \bigl[1\) , \( 0\) , \( a^{3} + a^{2} - 3 a - 3\) , \( -3 a^{3} + 4 a^{2} + 12 a - 19\) , \( -2 a^{2} - 2 a + 4\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph