Properties

Base field 4.4.5125.1
Label 4.4.5125.1-55.1-d
Conductor 55.1
Rank \( 0 \)

Related objects

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Base field 4.4.5125.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 6 x^{2} + 7 x + 11 \); class number \(1\).

Elliptic curves in class 55.1-d over 4.4.5125.1

Isogeny class 55.1-d contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
55.1-d1 \( \bigl[a^{3} - 4 a - 3\) , \( 0\) , \( a^{3} - 4 a - 3\) , \( a^{3} - 4 a - 3\) , \( a^{3} - 4 a - 2\bigr] \)
55.1-d2 \( \bigl[a^{3} - 4 a - 3\) , \( 0\) , \( a^{3} - 4 a - 3\) , \( -4 a^{3} + 16 a - 3\) , \( -24 a^{3} - 24 a^{2} + 99 a + 130\bigr] \)
55.1-d3 \( \bigl[a + 1\) , \( 0\) , \( a^{3} - 4 a - 3\) , \( -191 a^{3} + 389 a^{2} + 555 a - 1139\) , \( -2260 a^{3} + 4761 a^{2} + 6611 a - 13813\bigr] \)
55.1-d4 \( \bigl[a + 1\) , \( 0\) , \( a^{3} - 4 a - 3\) , \( -6 a^{3} - a^{2} + 25 a + 16\) , \( -86 a^{3} + 215 a^{2} + 239 a - 646\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph