Properties

Base field 4.4.5125.1
Label 4.4.5125.1-55.2-a
Conductor 55.2
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 55.2-a over 4.4.5125.1

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

Curve label Weierstrass Coefficients
55.2-a1 \( \bigl[a^{3} - 4 a - 4\) , \( -a - 1\) , \( a\) , \( 64 a^{3} - a^{2} - 383 a - 342\) , \( 655 a^{3} + 104 a^{2} - 3702 a - 3363\bigr] \)
55.2-a2 \( \bigl[a^{3} - 4 a - 4\) , \( -a - 1\) , \( a\) , \( -6 a^{3} - a^{2} + 32 a + 28\) , \( 45 a^{3} + 6 a^{2} - 259 a - 235\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph