Properties

Base field 3.3.257.1
Label 3.3.257.1-9.1-b
Conductor 9.1
Rank \( 1 \)

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 9.1-b over 3.3.257.1

Isogeny class 9.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
9.1-b1 \( \bigl[a^{2} - 2\) , \( -a^{2} + 2\) , \( a^{2} + a - 3\) , \( -998 a^{2} + 2900 a - 1562\) , \( -39467 a^{2} + 114933 a - 61916\bigr] \)
9.1-b2 \( \bigl[a^{2} - 2\) , \( -a^{2} + 2\) , \( a^{2} + a - 3\) , \( -88 a^{2} + 260 a - 152\) , \( 13 a^{2} - 45 a + 32\bigr] \)
9.1-b3 \( \bigl[a^{2} - 2\) , \( -a^{2} + 2\) , \( a^{2} + a - 3\) , \( -63 a^{2} + 180 a - 97\) , \( -601 a^{2} + 1748 a - 942\bigr] \)
9.1-b4 \( \bigl[a^{2} - 2\) , \( -a^{2} + 2\) , \( a^{2} + a - 3\) , \( -3 a^{2} + 5 a - 2\) , \( -18 a^{2} + 50 a - 27\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph