Properties

Base field 4.4.14272.1
Label 4.4.14272.1-17.1-b
Conductor 17.1
Rank \( 1 \)

Related objects

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Base field 4.4.14272.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 5 x^{2} + 2 x + 3 \); class number \(1\).

Elliptic curves in class 17.1-b over 4.4.14272.1

Isogeny class 17.1-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
17.1-b1 \( \bigl[2 a^{3} - 5 a^{2} - 6 a + 5\) , \( 0\) , \( 2 a^{3} - 5 a^{2} - 6 a + 5\) , \( -848 a^{3} + 2260 a^{2} + 2564 a - 3510\) , \( -22808 a^{3} + 61558 a^{2} + 69436 a - 95032\bigr] \)
17.1-b2 \( \bigl[2 a^{3} - 5 a^{2} - 6 a + 5\) , \( 0\) , \( 2 a^{3} - 5 a^{2} - 6 a + 5\) , \( -48 a^{3} + 130 a^{2} + 144 a - 215\) , \( -466 a^{3} + 1261 a^{2} + 1414 a - 1971\bigr] \)
17.1-b3 \( \bigl[2 a^{3} - 5 a^{2} - 6 a + 5\) , \( 0\) , \( 2 a^{3} - 5 a^{2} - 6 a + 5\) , \( -8 a^{3} + 20 a^{2} + 24 a - 35\) , \( -54 a^{3} + 149 a^{2} + 166 a - 231\bigr] \)
17.1-b4 \( \bigl[2 a^{3} - 5 a^{2} - 6 a + 5\) , \( 0\) , \( 2 a^{3} - 5 a^{2} - 6 a + 5\) , \( 2 a^{3} - 5 a^{2} - 6 a + 5\) , \( 2 a^{3} - 5 a^{2} - 6 a + 6\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph