Properties

Base field 3.3.1101.1
Label 3.3.1101.1-6.1-a
Conductor 6.1
Rank \( 1 \)

Related objects

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Base field 3.3.1101.1

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 9 x + 12 \); class number \(1\).

Elliptic curves in class 6.1-a over 3.3.1101.1

Isogeny class 6.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
6.1-a1 \( \bigl[a^{2} + 2 a - 7\) , \( a + 1\) , \( a\) , \( -12815463 a^{2} + 52787238 a - 49305624\) , \( -50792903895 a^{2} + 209217326538 a - 195418286610\bigr] \)
6.1-a2 \( \bigl[1\) , \( a^{2} - 8\) , \( a^{2} + a - 7\) , \( -5 a^{2} + 52 a - 105\) , \( -186 a^{2} + 572 a - 196\bigr] \)
6.1-a3 \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -801934 a^{2} + 3303175 a - 3085301\) , \( -1420574725 a^{2} + 5851385188 a - 5465453961\bigr] \)
6.1-a4 \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -50124 a^{2} + 206470 a - 192851\) , \( -22179850 a^{2} + 91359400 a - 85333743\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph