Properties

Base field 5.5.65657.1
Label 5.5.65657.1-37.1-b
Conductor 37.1
Rank not recorded

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Base field 5.5.65657.1

Generator \(a\), with minimal polynomial \( x^{5} - x^{4} - 5 x^{3} + 2 x^{2} + 5 x + 1 \); class number \(1\).

Elliptic curves in class 37.1-b over 5.5.65657.1

Isogeny class 37.1-b contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
37.1-b1 \( \bigl[0\) , \( -a^{3} + 4 a + 2\) , \( -2 a^{4} + 3 a^{3} + 9 a^{2} - 8 a - 7\) , \( -20 a^{4} + 24 a^{3} + 92 a^{2} - 55 a - 81\) , \( 136 a^{4} - 170 a^{3} - 637 a^{2} + 426 a + 579\bigr] \)
37.1-b2 \( \bigl[0\) , \( a^{4} - 2 a^{3} - 5 a^{2} + 6 a + 5\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 7 a - 4\) , \( 5 a^{4} - 8 a^{3} - 19 a^{2} + 22 a + 10\) , \( -5 a^{4} + 9 a^{3} + 17 a^{2} - 24 a - 6\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph