Properties

Base field 4.4.17609.1
Label 4.4.17609.1-14.1-d
Conductor 14.1
Rank \( 1 \)

Related objects

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Base field 4.4.17609.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 7 x^{2} + 10 x - 1 \); class number \(1\).

Elliptic curves in class 14.1-d over 4.4.17609.1

Isogeny class 14.1-d contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
14.1-d1 \( \bigl[1\) , \( -2 a^{3} - a^{2} + 12 a - 2\) , \( 2 a^{3} + a^{2} - 11 a + 2\) , \( -7 a^{3} + 47 a - 29\) , \( 2 a^{3} - 3 a^{2} - 13 a + 17\bigr] \)
14.1-d2 \( \bigl[2 a^{3} + a^{2} - 11 a + 3\) , \( a^{3} + a^{2} - 5 a - 2\) , \( a^{3} - 6 a + 3\) , \( 986 a^{3} + 480 a^{2} - 6186 a + 662\) , \( 25024 a^{3} + 12147 a^{2} - 157124 a + 16845\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph