Properties

Base field 4.4.2777.1
Label 4.4.2777.1-968.2-b
Conductor 968.2
Rank \( 0 \)

Related objects

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Base field 4.4.2777.1

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

Elliptic curves in class 968.2-b over 4.4.2777.1

Isogeny class 968.2-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
968.2-b1 \( \bigl[a^{3} - 4 a\) , \( a^{3} - 5 a - 2\) , \( a^{2} - 2\) , \( 214 a^{3} - 544 a^{2} - 30 a + 277\) , \( 1464 a^{3} - 3687 a^{2} - 276 a + 1917\bigr] \)
968.2-b2 \( \bigl[a^{3} - 4 a\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - a^{2} - 3 a + 2\) , \( -6 a^{3} + 9 a^{2} + 18 a - 15\) , \( -8 a^{3} + 13 a^{2} + 23 a - 22\bigr] \)
968.2-b3 \( \bigl[a^{3} - 3 a\) , \( -a^{3} + 4 a + 2\) , \( a^{3} - 3 a\) , \( -920 a^{3} + 1564 a^{2} + 2614 a - 2798\) , \( 20313 a^{3} - 34196 a^{2} - 58012 a + 59987\bigr] \)
968.2-b4 \( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( a^{3} - 4 a - 2\) , \( a^{3} - 3 a\) , \( -10 a^{3} + 106 a^{2} - 47 a - 348\) , \( -482 a^{3} + 804 a^{2} + 1370 a - 1417\bigr] \)
968.2-b5 \( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( a^{3} - 4 a - 2\) , \( a^{3} - 3 a\) , \( 30 a^{3} + a^{2} - 132 a - 98\) , \( -265 a^{3} + 57 a^{2} + 1077 a + 585\bigr] \)
968.2-b6 \( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( -a\) , \( a^{3} - 4 a\) , \( -23 a^{3} + 3 a^{2} - 3 a - 9\) , \( -130 a^{3} - 194 a^{2} + 136 a + 140\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph