Properties

Base field 3.3.733.1
Label 3.3.733.1-112.3-d
Conductor 112.3
Rank \( 0 \)

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 112.3-d over 3.3.733.1

Isogeny class 112.3-d contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
112.3-d1 \( \bigl[a^{2} - 4\) , \( a^{2} - 5\) , \( 0\) , \( 6522075544 a^{2} + 1162195248 a - 44285237232\) , \( 75145501189304 a^{2} + 13390483451933 a - 510241919992728\bigr] \)
112.3-d2 \( \bigl[a^{2} - 4\) , \( -a^{2} + a + 5\) , \( a^{2} + a - 4\) , \( 3542 a^{2} + 632 a - 24056\) , \( 192487 a^{2} + 34296 a - 1306992\bigr] \)
112.3-d3 \( \bigl[a^{2} + a - 4\) , \( -1\) , \( 0\) , \( 6 a^{2} + 4 a - 40\) , \( 32 a^{2} + 7 a - 216\bigr] \)
112.3-d4 \( \bigl[a\) , \( a^{2} - 5\) , \( a^{2} - 4\) , \( 318 a^{2} + 457 a - 1072\) , \( -167802 a^{2} - 254825 a + 532900\bigr] \)
112.3-d5 \( \bigl[a\) , \( a^{2} - 5\) , \( a^{2} - 4\) , \( -1387 a^{2} - 2108 a + 4408\) , \( -52665 a^{2} - 79956 a + 167308\bigr] \)
112.3-d6 \( \bigl[a\) , \( a^{2} - 5\) , \( a^{2} - 4\) , \( -22052 a^{2} - 33473 a + 70048\) , \( -3353096 a^{2} - 5090675 a + 10652372\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph