Properties

Base field 4.4.15952.1
Label 4.4.15952.1-12.1-a
Conductor 12.1
Rank \( 0 \)

Related objects

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Base field 4.4.15952.1

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

Elliptic curves in class 12.1-a over 4.4.15952.1

Isogeny class 12.1-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
12.1-a1 \( \bigl[a^{2} - 3\) , \( -a^{3} + 5 a + 2\) , \( a^{2} - a - 2\) , \( -5 a^{3} + 2 a^{2} + 30 a\) , \( -5 a^{3} + 6 a^{2} + 39 a - 3\bigr] \)
12.1-a2 \( \bigl[-a^{3} + a^{2} + 5 a - 1\) , \( a^{3} - 7 a\) , \( a^{2} - 3\) , \( 2 a^{3} - 16 a + 4\) , \( 2 a^{3} - 16 a + 4\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph