Properties

Base field 4.4.725.1
Label 4.4.725.1-121.2-a
Conductor 121.2
Rank not recorded

Related objects

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Base field 4.4.725.1

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

Elliptic curves in class 121.2-a over 4.4.725.1

Isogeny class 121.2-a contains 8 curves linked by isogenies of degrees dividing 20.

Curve label Weierstrass Coefficients
121.2-a1 \( \bigl[a^{2}\) , \( a^{3} - a^{2} - 2 a + 1\) , \( a^{3} - a^{2} - a + 2\) , \( -16720 a^{3} + 24671 a^{2} + 38355 a - 35026\) , \( -1387530 a^{3} + 2049643 a^{2} + 3184128 a - 2907368\bigr] \)
121.2-a2 \( \bigl[a^{2}\) , \( a^{3} - a^{2} - 2 a + 1\) , \( a^{3} - a^{2} - a + 2\) , \( -1280 a^{3} + 1411 a^{2} + 2605 a - 2256\) , \( -23574 a^{3} + 24161 a^{2} + 47564 a - 38706\bigr] \)
121.2-a3 \( \bigl[a^{2}\) , \( a^{3} - a^{2} - 2 a + 1\) , \( a^{3} - a^{2} - a + 2\) , \( -1040 a^{3} + 1521 a^{2} + 2360 a - 2201\) , \( -22150 a^{3} + 32546 a^{2} + 50676 a - 46325\bigr] \)
121.2-a4 \( \bigl[a^{2}\) , \( a^{3} - a^{2} - 2 a + 1\) , \( a^{3} - a^{2} - a + 2\) , \( -325 a^{3} + 501 a^{2} + 730 a - 741\) , \( 3802 a^{3} - 5685 a^{2} - 8677 a + 8158\bigr] \)
121.2-a5 \( \bigl[a^{2}\) , \( a^{3} - a^{2} - 2 a + 1\) , \( a^{3} - a^{2} - a + 2\) , \( -45 a^{3} + 81 a^{2} + 95 a - 146\) , \( -374 a^{3} + 588 a^{2} + 831 a - 909\bigr] \)
121.2-a6 \( \bigl[a^{2}\) , \( a^{3} - a^{2} - 2 a + 1\) , \( a^{3} - a^{2} - a + 2\) , \( -35 a^{3} + 41 a^{2} + 80 a - 71\) , \( -50 a^{3} + 83 a^{2} + 109 a - 102\bigr] \)
121.2-a7 \( \bigl[a^{2}\) , \( a^{3} - a^{2} - 2 a + 1\) , \( a^{3} - a^{2} - a + 2\) , \( -20 a^{3} + 31 a^{2} + 45 a - 46\) , \( 50 a^{3} - 75 a^{2} - 114 a + 108\bigr] \)
121.2-a8 \( \bigl[a^{2}\) , \( a^{3} - a^{2} - 2 a + 1\) , \( a^{3} - a^{2} - a + 2\) , \( a^{2} - 1\) , \( 2 a^{3} - 2 a^{2} - 4 a + 3\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 20 & 4 & 5 & 10 & 20 \\ 4 & 1 & 2 & 5 & 4 & 20 & 10 & 20 \\ 2 & 2 & 1 & 10 & 2 & 10 & 5 & 10 \\ 20 & 5 & 10 & 1 & 20 & 4 & 2 & 4 \\ 4 & 4 & 2 & 20 & 1 & 20 & 10 & 5 \\ 5 & 20 & 10 & 4 & 20 & 1 & 2 & 4 \\ 10 & 10 & 5 & 2 & 10 & 2 & 1 & 2 \\ 20 & 20 & 10 & 4 & 5 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph