Properties

Base field 4.4.5125.1
Label 4.4.5125.1-55.1-e
Conductor 55.1
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 55.1-e over 4.4.5125.1

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

Curve label Weierstrass Coefficients
55.1-e1 \( \bigl[a^{2} - 3\) , \( a^{3} - 2 a^{2} - 4 a + 4\) , \( 0\) , \( 22 a^{3} - 20 a^{2} - 95 a - 42\) , \( -107 a^{3} + 34 a^{2} + 540 a + 416\bigr] \)
55.1-e2 \( \bigl[a^{2} - 3\) , \( a^{3} - 2 a^{2} - 4 a + 4\) , \( 0\) , \( 2 a^{3} - 5 a^{2} - 5 a + 13\) , \( -2 a^{3} - 2 a^{2} + 13 a + 20\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph