Properties

Base field 3.3.316.1
Label 3.3.316.1-32.5-a
Conductor 32.5
Rank not recorded

Related objects

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Base field 3.3.316.1

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

Elliptic curves in class 32.5-a over 3.3.316.1

Isogeny class 32.5-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
32.5-a1 \( \bigl[a^{2} - 3\) , \( a^{2} + a - 3\) , \( a + 1\) , \( 11637 a^{2} - 6160 a - 49447\) , \( 996638 a^{2} - 527538 a - 4234857\bigr] \)
32.5-a2 \( \bigl[a^{2} - 3\) , \( -a^{2} + a + 3\) , \( a + 1\) , \( -5 a^{2} + 18\) , \( -3 a^{2} + 2 a + 13\bigr] \)
32.5-a3 \( \bigl[a + 1\) , \( -a\) , \( a^{2} + a - 2\) , \( 623 a^{2} - 451 a - 2866\) , \( -13706 a^{2} + 8249 a + 60042\bigr] \)
32.5-a4 \( \bigl[a + 1\) , \( -a\) , \( a^{2} + a - 2\) , \( 68 a^{2} - 46 a - 306\) , \( 141 a^{2} - 62 a - 576\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 4 & 2 \\ 4 & 1 & 4 & 2 \\ 4 & 4 & 1 & 2 \\ 2 & 2 & 2 & 1 \end{array}\right)\)

Isogeny graph