Properties

Base field 3.3.316.1
Label 3.3.316.1-34.1-a
Conductor 34.1
Rank not recorded

Related objects

Learn more about

Base field 3.3.316.1

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

Elliptic curves in class 34.1-a over 3.3.316.1

Isogeny class 34.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
34.1-a1 \( \bigl[1\) , \( a^{2} - 4\) , \( a^{2} + a - 3\) , \( 31 a^{2} - 17 a - 132\) , \( -112 a^{2} + 58 a + 473\bigr] \)
34.1-a2 \( \bigl[1\) , \( 0\) , \( a^{2} - 3\) , \( 68502161 a^{2} - 36259336 a - 291075321\) , \( -451289674314 a^{2} + 238875107051 a + 1917593249559\bigr] \)
34.1-a3 \( \bigl[1\) , \( 0\) , \( a^{2} - 3\) , \( 4281891 a^{2} - 2266481 a - 18194366\) , \( -7049373774 a^{2} + 3731350409 a + 29953779855\bigr] \)
34.1-a4 \( \bigl[1\) , \( -a^{2} - a + 2\) , \( a^{2} - 3\) , \( 34458467957 a^{2} - 18239438694 a - 146418873583\) , \( -9030431019955685 a^{2} + 4779956864569160 a + 38371570523670525\bigr] \)

Rank

Rank not yet determined.

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