Properties

Base field 3.3.321.1
Label 3.3.321.1-9.3-b
Conductor 9.3
Rank \( 1 \)

Related objects

Learn more

Base field 3.3.321.1

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

Elliptic curves in class 9.3-b over 3.3.321.1

Isogeny class 9.3-b contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
9.3-b1 \( \bigl[0\) , \( a^{2} - 4\) , \( 1\) , \( -a^{2} + a + 5\) , \( -a - 2\bigr] \)
9.3-b2 \( \bigl[0\) , \( a^{2} - 4\) , \( a + 1\) , \( -a^{2} + a + 5\) , \( 67166 a^{2} + 98095 a - 27300\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph