Properties

Base field 4.4.9248.1
Label 4.4.9248.1-26.1-b
Conductor 26.1
Rank \( 1 \)

Related objects

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Base field 4.4.9248.1

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

Elliptic curves in class 26.1-b over 4.4.9248.1

Isogeny class 26.1-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
26.1-b1 \( \bigl[a + 1\) , \( -a^{3} + a^{2} + 4 a - 4\) , \( 1\) , \( -92 a^{3} + 43 a^{2} + 426 a - 275\) , \( -353 a^{3} + 162 a^{2} + 1654 a - 1064\bigr] \)
26.1-b2 \( \bigl[a + 1\) , \( -a^{2} + 3\) , \( a\) , \( 530 a^{3} + 349 a^{2} - 2419 a - 1598\) , \( 11558 a^{3} + 7652 a^{2} - 52724 a - 34910\bigr] \)
26.1-b3 \( \bigl[a + 1\) , \( -a^{2} + 3\) , \( a\) , \( 15 a^{3} + 9 a^{2} - 69 a - 43\) , \( -16 a^{3} - 11 a^{2} + 73 a + 49\bigr] \)
26.1-b4 \( \bigl[a + 1\) , \( -a^{3} + a^{2} + 4 a - 4\) , \( 1\) , \( -37 a^{3} + 23 a^{2} + 166 a - 110\) , \( 290 a^{3} - 191 a^{2} - 1321 a + 874\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 6 & 3 \\ 2 & 1 & 3 & 6 \\ 6 & 3 & 1 & 2 \\ 3 & 6 & 2 & 1 \end{array}\right)\)

Isogeny graph