Properties

Base field 4.4.5125.1
Label 4.4.5125.1-55.2-e
Conductor 55.2
Rank \( 1 \)

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 55.2-e over 4.4.5125.1

Isogeny class 55.2-e contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
55.2-e1 \( \bigl[a^{2} - 4\) , \( a^{3} - 5 a - 4\) , \( a^{2} - 3\) , \( -22 a^{3} + 47 a^{2} + 69 a - 141\) , \( 67 a^{3} - 189 a^{2} - 181 a + 592\bigr] \)
55.2-e2 \( \bigl[a^{2} - 4\) , \( a^{3} - 5 a - 4\) , \( a^{2} - 3\) , \( -2 a^{3} + 2 a^{2} + 9 a - 1\) , \( 2 a^{3} - 5 a^{2} - 7 a + 13\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph