Properties

Base field 4.4.5125.1
Label 4.4.5125.1-55.1-f
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-f over 4.4.5125.1

Isogeny class 55.1-f contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
55.1-f1 \( \bigl[a^{3} - 4 a - 4\) , \( 1\) , \( 1\) , \( -218 a^{3} - 146 a^{2} + 869 a + 827\) , \( -4041 a^{3} - 2859 a^{2} + 16568 a + 16518\bigr] \)
55.1-f2 \( \bigl[1\) , \( a^{3} - 4 a - 5\) , \( a^{3} - 5 a - 4\) , \( 7 a^{3} - 24 a^{2} + 42\) , \( 14 a^{3} - 54 a^{2} + 8 a + 98\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph