Properties

Base field 3.3.316.1
Label 3.3.316.1-32.4-a
Conductor 32.4
Rank \( 0 \)

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 32.4-a over 3.3.316.1

Isogeny class 32.4-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
32.4-a1 \( \bigl[a^{2} + a - 2\) , \( a^{2} - 3\) , \( 0\) , \( 2856 a^{2} - 1512 a - 12136\) , \( 109938 a^{2} - 58192 a - 467142\bigr] \)
32.4-a2 \( \bigl[a^{2} + a - 2\) , \( a^{2} - 3\) , \( 0\) , \( 616 a^{2} - 317 a - 2601\) , \( -10508 a^{2} + 5572 a + 44668\bigr] \)
32.4-a3 \( \bigl[a^{2} + a - 2\) , \( -a - 1\) , \( a^{2} + a - 2\) , \( -15 a^{2} - 20 a + 13\) , \( 111 a^{2} + 149 a - 95\bigr] \)
32.4-a4 \( \bigl[0\) , \( -a^{2} - a + 2\) , \( 0\) , \( 190001 a^{2} - 100568 a - 807336\) , \( -65837291 a^{2} + 34848768 a + 279751899\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph