Properties

Base field 3.3.733.1
Label 3.3.733.1-8.1-c
Conductor 8.1
Rank not recorded

Related objects

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Base field 3.3.733.1

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 7 x + 8 \); class number \(1\).

Elliptic curves in class 8.1-c over 3.3.733.1

Isogeny class 8.1-c contains 4 curves linked by isogenies of degrees dividing 10.

Curve label Weierstrass Coefficients
8.1-c1 \( \bigl[a^{2} - 5\) , \( -a^{2} + a + 6\) , \( 0\) , \( -152999337 a^{2} - 232283388 a + 486059637\) , \( 1903534097274 a^{2} + 2889942990612 a - 6047288000831\bigr] \)
8.1-c2 \( \bigl[a^{2} - 5\) , \( -a^{2} + a + 6\) , \( 0\) , \( -9319242867 a^{2} - 14148462393 a + 29606060477\) , \( -915329396489703 a^{2} - 1389651899205825 a + 2907886170331433\bigr] \)
8.1-c3 \( \bigl[1\) , \( -a^{2} + a + 4\) , \( a\) , \( a^{2} - 3 a - 3\) , \( -a^{2} + a + 1\bigr] \)
8.1-c4 \( \bigl[1\) , \( -a^{2} + a + 4\) , \( a\) , \( -174 a^{2} - 328 a + 377\) , \( -3028 a^{2} - 5091 a + 8285\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 2 & 10 \\ 5 & 1 & 10 & 2 \\ 2 & 10 & 1 & 5 \\ 10 & 2 & 5 & 1 \end{array}\right)\)

Isogeny graph