Properties

Base field 4.4.9248.1
Label 4.4.9248.1-16.3-a
Conductor 16.3
Rank \( 0 \)

Related objects

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Base field 4.4.9248.1

Generator \(a\), with minimal polynomial \( x^{4} - 5 x^{2} + 2 \); class number \(1\).

Elliptic curves in class 16.3-a over 4.4.9248.1

Isogeny class 16.3-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
16.3-a1 \( \bigl[a^{2} + a - 2\) , \( -a^{2} + a + 4\) , \( a + 1\) , \( -10 a^{3} - 24 a^{2} - 3 a + 8\) , \( 47 a^{3} + 92 a^{2} - 47 a - 63\bigr] \)
16.3-a2 \( \bigl[a^{2} + a - 2\) , \( a^{3} + a^{2} - 5 a - 3\) , \( a^{3} - 4 a + 1\) , \( -119 a^{3} - 79 a^{2} + 544 a + 365\) , \( 17497 a^{3} + 11587 a^{2} - 79812 a - 52851\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph