Properties

Base field 4.4.8112.1
Label 4.4.8112.1-9.1-a
Conductor 9.1
Rank \( 0 \)

Related objects

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Base field 4.4.8112.1

Generator \(a\), with minimal polynomial \( x^{4} - 5 x^{2} + 3 \); class number \(1\).

Elliptic curves in class 9.1-a over 4.4.8112.1

Isogeny class 9.1-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
9.1-a1 \( \bigl[a^{2} + a - 3\) , \( a^{2} - 3\) , \( a^{3} + a^{2} - 3 a - 3\) , \( -3 a^{3} - 4 a^{2} + 6 a - 3\) , \( -3 a^{3} - 14 a^{2} - 6 a + 12\bigr] \)
9.1-a2 \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} + a^{2} - 3 a - 3\) , \( 16 a^{3} + 15 a^{2} - 69 a - 60\) , \( 68 a^{3} + 57 a^{2} - 291 a - 243\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph