Properties

Base field 3.3.1129.1
Label 3.3.1129.1-9.2-b
Conductor 9.2
Rank \( 1 \)

Related objects

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Base field 3.3.1129.1

Generator \(a\), with minimal polynomial \( x^{3} - 7 x - 3 \); class number \(1\).

Elliptic curves in class 9.2-b over 3.3.1129.1

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

Curve label Weierstrass Coefficients
9.2-b1 \( \bigl[1\) , \( -a^{2} + a + 4\) , \( a^{2} - a - 4\) , \( -15 a^{2} + 34 a + 24\) , \( 96 a^{2} - 230 a - 121\bigr] \)
9.2-b2 \( \bigl[1\) , \( -a^{2} + a + 4\) , \( a^{2} - a - 4\) , \( -240 a^{2} + 574 a + 304\) , \( 4880 a^{2} - 11700 a - 6108\bigr] \)
9.2-b3 \( \bigl[1\) , \( -a^{2} + a + 4\) , \( a^{2} - a - 4\) , \( -250 a^{2} + 599 a + 314\) , \( 4473 a^{2} - 10722 a - 5605\bigr] \)
9.2-b4 \( \bigl[1\) , \( -a^{2} + a + 4\) , \( a^{2} - a - 4\) , \( -3830 a^{2} + 9189 a + 4774\) , \( 297403 a^{2} - 713078 a - 372099\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph