Properties

Base field 4.4.5125.1
Label 4.4.5125.1-29.2-b
Conductor 29.2
Rank \( 1 \)

Related objects

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Base field 4.4.5125.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 6 x^{2} + 7 x + 11 \); class number \(1\).

Elliptic curves in class 29.2-b over 4.4.5125.1

Isogeny class 29.2-b contains 2 curves linked by isogenies of degree 7.

Curve label Weierstrass Coefficients
29.2-b1 \( \bigl[a^{2} - a - 3\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{3} - 4 a - 3\) , \( 2 a^{3} - a^{2} - 11 a - 6\) , \( -5 a^{3} - a^{2} + 27 a + 24\bigr] \)
29.2-b2 \( \bigl[a^{3} - a^{2} - 4 a\) , \( -a^{3} + a^{2} + 4 a\) , \( a + 1\) , \( 1230 a^{3} - 3982 a^{2} - 2398 a + 11270\) , \( -12237 a^{3} + 35584 a^{2} + 43296 a - 135242\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph