Properties

Base field 3.3.257.1
Label 3.3.257.1-9.2-a
Conductor 9.2
Rank \( 0 \)

Related objects

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Base field 3.3.257.1

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

Elliptic curves in class 9.2-a over 3.3.257.1

Isogeny class 9.2-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
9.2-a1 \( \bigl[a^{2} + a - 3\) , \( -a^{2} + a + 3\) , \( a^{2} - 2\) , \( 2 a^{2} + 2 a - 6\) , \( -8 a^{2} - 11 a + 9\bigr] \)
9.2-a2 \( \bigl[a^{2} + a - 3\) , \( -a^{2} + a + 3\) , \( a^{2} - 2\) , \( -3 a^{2} - 3 a + 9\) , \( -7 a^{2} - 6 a + 12\bigr] \)
9.2-a3 \( \bigl[1\) , \( -a^{2} - a + 2\) , \( a\) , \( 29 a^{2} - 9 a - 123\) , \( 148 a^{2} - 17 a - 575\bigr] \)
9.2-a4 \( \bigl[1\) , \( -a^{2} - a + 2\) , \( a\) , \( -a^{2} - 4 a - 3\) , \( 15 a^{2} + 14 a - 29\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph