Properties

Base field 3.3.49.1
Label 3.3.49.1-41.3-a
Conductor 41.3
Rank not recorded

Related objects

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Base field 3.3.49.1

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

Elliptic curves in class 41.3-a over 3.3.49.1

Isogeny class 41.3-a contains 4 curves linked by isogenies of degrees dividing 10.

Curve label Weierstrass Coefficients
41.3-a1 \( \bigl[1\) , \( a^{2} - a - 3\) , \( 0\) , \( -91 a^{2} + 101 a - 68\) , \( -646 a^{2} + 852 a - 304\bigr] \)
41.3-a2 \( \bigl[1\) , \( a^{2} - a - 3\) , \( 0\) , \( -71 a^{2} + 146 a - 43\) , \( -456 a^{2} + 1027 a - 381\bigr] \)
41.3-a3 \( \bigl[1\) , \( a^{2} - a - 3\) , \( 0\) , \( 4 a^{2} - 4 a - 8\) , \( -11 a^{2} + 7 a + 26\bigr] \)
41.3-a4 \( \bigl[1\) , \( a^{2} - a - 3\) , \( 0\) , \( -a^{2} + a + 2\) , \( 0\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph