Properties

Base field 4.4.17428.1
Label 4.4.17428.1-8.3-a
Conductor 8.3
Rank \( 1 \)

Related objects

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Base field 4.4.17428.1

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

Elliptic curves in class 8.3-a over 4.4.17428.1

Isogeny class 8.3-a contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
8.3-a1 \( \bigl[a^{2} - 3\) , \( -a^{3} + 5 a + 2\) , \( a^{3} + a^{2} - 3 a - 3\) , \( -7 a^{3} - 7 a^{2} + 25 a + 20\) , \( 6 a^{3} + 10 a^{2} - 11 a - 12\bigr] \)
8.3-a2 \( \bigl[a^{3} - 4 a - 1\) , \( -a^{2} + a + 4\) , \( a + 1\) , \( -a^{3} - 5 a^{2} + 5 a + 25\) , \( -3 a^{2} + 14\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph