Properties

Base field 6.6.1241125.1
Label 6.6.1241125.1-41.1-a
Conductor 41.1
Rank not recorded

Related objects

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Base field 6.6.1241125.1

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

Elliptic curves in class 41.1-a over 6.6.1241125.1

Isogeny class 41.1-a contains 2 curves linked by isogenies of degree 7.

Curve label Weierstrass Coefficients
41.1-a1 \( \bigl[-5 a^{5} + 2 a^{4} + 34 a^{3} - 2 a^{2} - 52 a - 19\) , \( a^{3} - a^{2} - 3 a + 1\) , \( a + 1\) , \( -4178 a^{5} + 5149 a^{4} + 22801 a^{3} - 19626 a^{2} - 21217 a - 3693\) , \( -269508 a^{5} + 337696 a^{4} + 1461510 a^{3} - 1289635 a^{2} - 1338554 a - 220717\bigr] \)
41.1-a2 \( \bigl[-5 a^{5} + 2 a^{4} + 34 a^{3} - 2 a^{2} - 52 a - 19\) , \( a^{3} - a^{2} - 3 a + 1\) , \( a + 1\) , \( 42 a^{5} - a^{4} - 304 a^{3} - 61 a^{2} + 513 a + 222\) , \( 107 a^{5} - 33 a^{4} - 729 a^{3} - 2 a^{2} + 1128 a + 453\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph