Properties

Base field 3.3.49.1
Label 3.3.49.1-71.3-a
Conductor 71.3
Rank not recorded

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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 71.3-a over 3.3.49.1

Isogeny class 71.3-a contains 4 curves linked by isogenies of degrees dividing 10.

Curve label Weierstrass Coefficients
71.3-a1 \( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} - 1\) , \( 4 a^{2} - 10 a - 44\) , \( -32 a^{2} - 61 a - 73\bigr] \)
71.3-a2 \( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} - 1\) , \( -a^{2} + 1\) , \( 0\bigr] \)
71.3-a3 \( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} - 1\) , \( -11 a^{2} - 5 a + 6\) , \( 18 a^{2} + 12 a - 9\bigr] \)
71.3-a4 \( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} - 1\) , \( -221 a^{2} - 190 a + 81\) , \( -2926 a^{2} - 2384 a + 1532\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph