Properties

Base field 6.6.1397493.1
Label 6.6.1397493.1-37.1-a
Conductor 37.1
Rank not recorded

Related objects

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Base field 6.6.1397493.1

Generator \(a\), with minimal polynomial \( x^{6} - 3 x^{5} - 3 x^{4} + 10 x^{3} + 3 x^{2} - 6 x + 1 \); class number \(1\).

Elliptic curves in class 37.1-a over 6.6.1397493.1

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

Curve label Weierstrass Coefficients
37.1-a1 \( \bigl[a^{4} - 2 a^{3} - 2 a^{2} + 3 a - 1\) , \( -a^{4} + 2 a^{3} + 2 a^{2} - 3 a + 2\) , \( a^{3} - a^{2} - 2 a + 1\) , \( -4 a^{4} + 8 a^{3} + 9 a^{2} - 12 a + 2\) , \( -2 a^{4} + 3 a^{3} + 6 a^{2} - 4 a\bigr] \)
37.1-a2 \( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 2\) , \( a^{4} - 4 a^{3} + 9 a - 1\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 6 a^{2} + 9 a - 2\) , \( -10 a^{5} + 22 a^{4} + 51 a^{3} - 73 a^{2} - 89 a + 22\) , \( -38 a^{5} + 99 a^{4} + 142 a^{3} - 286 a^{2} - 220 a + 54\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph