Properties

Base field 4.4.17428.1
Label 4.4.17428.1-9.1-d
Conductor 9.1
Rank \( 0 \)

Related objects

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Base field 4.4.17428.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 6 x^{2} + 4 x + 6 \); class number \(1\).

Elliptic curves in class 9.1-d over 4.4.17428.1

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

Curve label Weierstrass Coefficients
9.1-d1 \( \bigl[a^{3} - 4 a\) , \( a^{2} + a - 3\) , \( a^{3} - 3 a - 1\) , \( 5 a^{3} - 5 a^{2} - 15 a + 12\) , \( 11 a^{3} - 11 a^{2} - 61 a + 77\bigr] \)
9.1-d2 \( \bigl[a\) , \( -a^{3} - a^{2} + 4 a + 3\) , \( a^{2} + a - 3\) , \( -417 a^{3} - 570 a^{2} + 1152 a + 1056\) , \( -11884 a^{3} - 16264 a^{2} + 32779 a + 30101\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph