Properties

Base field 4.4.16448.1
Label 4.4.16448.1-20.2-d
Conductor 20.2
Rank \( 1 \)

Related objects

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Base field 4.4.16448.1

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

Elliptic curves in class 20.2-d over 4.4.16448.1

Isogeny class 20.2-d contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
20.2-d1 \( \bigl[0\) , \( a^{2} - 2 a - 3\) , \( a^{3} - 2 a^{2} - 5 a\) , \( -21 a^{3} + 31 a^{2} + 142 a + 77\) , \( 49 a^{3} - 71 a^{2} - 334 a - 183\bigr] \)
20.2-d2 \( \bigl[a^{3} - 3 a^{2} - 2 a + 2\) , \( 0\) , \( a^{3} - 3 a^{2} - 2 a + 2\) , \( 5 a^{3} + 4 a^{2} - 2\) , \( 8 a^{3} + 16 a^{2} - 6\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph