Properties

Base field 4.4.9248.1
Label 4.4.9248.1-16.3-d
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-d over 4.4.9248.1

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

Curve label Weierstrass Coefficients
16.3-d1 \( \bigl[a^{2} + a - 2\) , \( -a^{3} - a^{2} + 4 a + 4\) , \( a^{3} + a^{2} - 3 a - 3\) , \( 8 a^{3} - 26 a^{2} + 12 a + 8\) , \( -71 a^{3} + 145 a^{2} + 51 a - 83\bigr] \)
16.3-d2 \( \bigl[a^{2} + a - 2\) , \( a^{3} + a^{2} - 5 a - 3\) , \( a^{2} - 3\) , \( 117 a^{3} - 78 a^{2} - 532 a + 361\) , \( -17215 a^{3} + 11402 a^{2} + 78529 a - 52007\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph