Properties

Base field 4.4.13824.1
Label 4.4.13824.1-9.1-a
Conductor 9.1
Rank \( 1 \)

Related objects

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Base field 4.4.13824.1

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

Elliptic curves in class 9.1-a over 4.4.13824.1

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

Curve label Weierstrass Coefficients
9.1-a1 \( \bigl[a^{2} - 2\) , \( a - 1\) , \( a^{3} + a^{2} - 4 a - 3\) , \( -5 a^{3} - 2 a^{2} + 15 a - 9\) , \( -251 a^{3} + 294 a^{2} + 1198 a - 1369\bigr] \)
9.1-a2 \( \bigl[a^{2} - 2\) , \( -a^{3} - a^{2} + 4 a + 2\) , \( a^{3} + a^{2} - 4 a - 3\) , \( 13 a^{3} - 11 a^{2} - 36 a - 6\) , \( 37 a^{3} - 104 a^{2} - 23 a + 158\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph