Properties

Base field 6.6.1312625.1
Label 6.6.1312625.1-41.1-e
Conductor 41.1
Rank \( 0 \)

Related objects

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Base field 6.6.1312625.1

Generator \(a\), with minimal polynomial \( x^{6} - x^{5} - 7 x^{4} + 7 x^{3} + 12 x^{2} - 12 x - 1 \); class number \(1\).

Elliptic curves in class 41.1-e over 6.6.1312625.1

Isogeny class 41.1-e contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
41.1-e1 \( \bigl[a^{3} - 2 a + 2\) , \( a^{5} + a^{4} - 8 a^{3} - 4 a^{2} + 14 a - 1\) , \( -a^{5} + 7 a^{3} + a^{2} - 10 a - 2\) , \( -6 a^{5} + 5 a^{4} + 32 a^{3} - 19 a^{2} - 28 a - 4\) , \( a^{5} + 10 a^{4} - 18 a^{3} - 44 a^{2} + 62 a + 8\bigr] \)
41.1-e2 \( \bigl[a^{3} - 2 a + 2\) , \( a^{5} + a^{4} - 8 a^{3} - 4 a^{2} + 14 a - 1\) , \( -a^{5} + 7 a^{3} + a^{2} - 10 a - 2\) , \( -a^{5} + 7 a^{3} + a^{2} - 13 a + 1\) , \( -3 a^{5} + 2 a^{4} + 18 a^{3} - 6 a^{2} - 22 a - 2\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph